

\noindent{\bf Trait�s recommand�s :}
\newline
\newline

BREZIS, H. Analyse fonctionnelle: th�orie et applications, Paris, Masson, 1983.
RUDIN, W. Real and Complex Analysis, New York, McGraw-Hill, 1966.
SCHWARTZ L. : Analyse I : th�ories des ensembles et topologie, HERMANN, Paris 1991 [10 SCH 00 F]

L. Schwartz Analyse : Topologie g�n�rale et analyse fonctionnelle, Hermann, Enseignement des Sciences, 1970.
\newline

\newline
J.M. Bony, Cours d'analyse de l'Ecole Polytechnique, Ecole
Polytechnique, 1994 (polycopi�).
\newline
G. Choquet, Cours de Topologie, seconde {�}dition, Masson, 1992.
\newline
J. Dixmier, Topologie G�n�rale, Masson.
\newline
N. Bourbaki, Topologie G�n�rale, Hermann, Paris.
\newline
T.W. K\ooo rner, Fourier Analysis, Cambridge University Press,
1988.
\newline
J. Neveu,  Bases math�matiques du calcul des probabilit�s, Masson,
1970.
\newline
W. Rudin, Real and complex analysis, Mc-Graw-Hill, 1966,
traduction fran\c caise Masson 1980.
\newline
W. Rudin, Functional Analysis, Mc-Graw-Hill, 1980.
\newline
\newline
\noindent{\bf Autres sources}
\newline
\newline
F. H�lein, Notes de cours, ENS Cachan, 1996 (manuscrit).
\newline
Y. Meyer, cours de DEA ondelettes 94-97 (manuscrits).
\newline
\newline
\noindent{\bf Articles en rapport avec les exp�riences num�riques
pr�sent�es}
\newline
\newline
P. Thevenaz, M. Unser, et L. Yaroslavsky, Convolution-based
interpolation for fast, high-quality rotation of images, IEEE
Trans. Image Processing, vol. 4, pp. 1371--1381, Oct.
1995.\newline J. J. Van Wijk, Spot Noise: Texture Synthesis for
Data Visualisation, Computer
  Graphics 1991, volume 25, numero 4, pp 309-317.

Introduction to Functional Analysis (Oxford Graduate Texts in
Mathematics) Reinhard Meise, Dietmar Vogt, M.S. Ramanujan
(Translator) Book Description The book is written for students of
mathematics and physics who have a basic knowledge of analysis and
linear algebra. It can be used as a textbook for courses and/or
seminars in functional analysis. Starting from metric spaces it
proceeds quickly to the central results of the field, including
the theorem of Hahn Banach. The spaces (p Lp (X,(), C(X)' and
Sobolov spaces are introduced. A chapter on spectral theory
contains the Riesz theory of compact operators, basic facts on
Banach and C*-algebras and the spectral representation for bounded
normal and unbounded self-adjoint operators in Hilbert spaces. An
introduction to locally convex spaces and their duality theory
provides the basis for a comprehensive treatment of Fr�chet spaces
and their duals. In particular recent results on sequences spaces,
linear topological invariants and short exact sequences of Fr�chet
spaces and the splitting of such sequences are presented. These
results are not contained in any o this field.

Synopsis Written for students of mathematics and physics who have
a basic knowledge of analysis and linear algebra, this book can be
used as a textbook for courses and/or seminars in functional
analysis. Starting from metric spaces it proceeds quickly to the
central results of the field, including the theorem of
Hahn-Banach. The spaces ( p L p ( X ,(), C ( X )' and Sebolov
spaces are introduced. A chapter on spectral theory contains the
Riesz theory of compact operators, basic facts on Banach and
C-algebras and the spectral representation for bounded normal and
unbounded self-adjoint operators in Hilbert spaces. An
introduction to locally convex spaces and their duality theory
provides the basis for a comprehensive treatment of Frechet spaces
and their duals. In particular recent results on sequences spaces,
linear topological invariants and short exact sequences of Frechet
spaces and the splitting of such sequences are presented.

A Gentle Introduction

    to Functional Analysis



By Dzung Minh Ha

Tentative publication date: summer, 2004

A student-friendly but rigorous book aimed primarily at third or
fourth year undergraduates. The pace is slow but thorough, with an
abundance of motivations, examples, and counterexamples. Arguments
used within proofs are explicitly cited, with references to where
they were first proved. Many examples have solutions that make use
of several results or concepts, so that students can see how
various techniques can blend together into one.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    Metric spaces

        Separable metric spaces
        Separability of l-p and non-separability of l-infinity
        Equivalent formulations for compactness
        Banach's fixed point theorem
        Baire's category theorem
        Sets of discontinuities
        Equicontinuity and the uniformed boundedness principles
        The Arzela-Ascoli theorem
        Dini's theorem

    Normed spaces

        Equivalence of norms
        Characterizations for finite-dimensional normed spaces
        Infinite series in Banach spaces and the Weierstrass M-test
        Riesz's lemma
        Schauder bases
        A Schauder basis for C[a,b]
        Quotient normed spaces
        Uncountabilty of Hamel bases for infinite-dimensional Banach spaces

    Linear operators

        Bounded linear operators
        Complementary subspaces and projections
        Linear homeomorphisms
        Isometric isomorphisms
        Factoring through the quotient maps
        Linear functionals and hyperplanes
        Characterizations of finite-dimensionality of normed spaces using linear functionals
        The space B(X,Y) and some fundamentals on spectral values
        The spectral radius formula

        (Scroll down for more.)

If you would like to be notified when this book becomes available, please sign up here.






























 Dual spaces

    Dual space of finite-dimensional normed space
    Dual spaces of some subspaces of l-infinity and l-p spaces
    Dual space of C[a,b]
    Annihilators and the conjugate map of a bounded linear operator (Banach adjoint)
    Necessary and sufficient conditions on the solvability of Tx=y
    Dual spaces of closed subspaces
    l^p and l^2 are not linearly homeomorphic
    Biduality and reflexivity
    Reflexivity of l^p and non-reflexivity of l^1
    Relationships between the relexivity of X and X^*
    Some characterizations of reflexivity in terms of saturated and total sets

Inner products and Hilbert spaces

    Orthogonality
    Bessel's inequality
    The projection theorem
    The minimum distance theorem
    Riesz representation theorem
    Bounded bilinear forms
    Some characterizations for Hilbert spaces
    Orthonormal sets
    Existence of Hilbert bases (maximal orthonormal sets)
    Equivalent formulations for Hilbert bases
    Parseval's theorem
    Riesz-Fischer theorem
    Closed complementary subspaces and projections
    Reflexivity of Hilbert spaces
    Classifications of Hilbert spaces
    Hamel bases versus Hilbert bases
    Weak completeness of Hilbert spaces

Weak convergence

    Weak convergence in l^p
    Weak completeness of reflexive normed spaces
    Schur's theorem on the equivalence of weak and strong convergence in l^1
    A Bolzano-Weierstrass theorem for weak convergence

Other topics

    Hahn-Banach theorem and its consequences
    Markov-Kakutani fixed point theorem
    Banach-Steinhaus theorem
    Divergence of Fourier series
    Open mapping theorem
    Closed graph theorem
    Closed complementary subspaces and continuous projections
    Continuity of coefficient functionals
    Finite-rank and compact operators
    The Bolzano-Weierstrass theorem
    Heine-Borel theorem
    Weierstrass approximation theorem
    Korovkin's theorem
    Bernstein's theorem
    Stone-Weierstrass theorem
    Linear functionals and Gramm's determinants
    Muntz's theorem
    Classification of closures of algebras in C(X)
    Classification of maximal ideals in C(X)

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    C. Gofman and G. Pedrick A First Course in Functional Analysis (Prentice Hall 1965)
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
         Functional Analysis
Peter D. Lax
ISBN: 0-471-55604-1
Hardcover
608 pages
March 2002
CDN $144.99 Add to Cart


Description
Table of Contents
Reviews

    Foreword.

Linear Spaces.

Linear Maps.

The Hahn-Banach Theorem.

Applications of the Hahn-Banach Theorem.

Normed Linear Spaces.

Hilbert Space.

Applications of Hilbert Space Results.

Duals of Normed Linear Space.

Applicaitons of Duality.

Weak Convergence.

Applications of Weak Convergence.

The Weak and Weak* Topologies.

Locally Convex Topologies and the Krein-Milman Theorem.

Examples of Convex Sets and their Extreme Points.

Bounded Linear Maps.

Examples of Bounded Linear Maps.

Banach Algebras and their Elementary Spectral Theory.

Gelfand's Theory of Commutative Banach Algebras.

Applications of Gelfand's Theory of Commutative Banach Algebras.

Examples of Operators and their Spectra.

Compact Maps.

Examples of Compact Operators.

Positive Compact Operators.

Fredholm's Theory of Integral Equations.

Invariant Subspaces.

Harmonic Analysis on a Halfline.

Index Theory.

Compact Symmetric Operators in Hilbert Space.

Examples of Compact Symmetric Operators.

Trace Class and Trace Formula.

Spectral Theory of Symmetric, Normal and Unitary Operators.

Spectral Theory of Self-Adjoint Operators.

Examples of Self-Adjoint Operators.

Semigroups of Operators.

Groups of Unitary Operators.

Examples of Strongly Continuous Semigroups.

Scattering Theory.

A Theorem of Beurling.

Appendix A: The Riesz-Kakutani Representation Theorem.

Appendix B: Theory of Distributions.

Appendix C: Zorn's Lemma.

Author Index.

Subject Index.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Introduction to Fourier Analysis by Norman Morrison
 (Author) Based
on a one-semester course originated by Morrison at the U. of Cape
Town, South Africa, this text covers all the core principles of
electrical engineering contained in Fourier analysis, including
the time and frequency domains, the representation of waveforms in
terms of complex exponentials and sinusoids, complex exponentials
and sinusoids as the eigenfunctions of linear systems,
convolution, impulse response and the frequency transfer function,
magnitude and phase spectra, and modulation and demodulation.
Disks (PC and Mac) included. Annotation copyright Book News, Inc.
Portland, Or.

The publisher, John Wiley & Sons 1994
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
ntroduction to Fourier Analysis, Solutions Manual
Norman Morrison
ISBN: 0-471-12848-1
Background.

Fourier Series for Periodic Functions.

The Fourier Integral.

Fourier Transforms of Some Important Functions.

The Method of Successive Differentiation.

Frequency-Domain Analysis.

Time-Domain Analysis.

The Properties.

The Sampling Theorems.

DISCRETE FOURIER ANALYSIS.

The Discrete Fourier Transform.

Inside the Fast Fourier Transform.

The Discrete Fourier Transform as an Estimator.

The Errors in Fast Fourier Transform Estimation.

The Four Kinds of Convolution.

Emulating Dirac Deltas and Differentiation on the Fast Fourier Transform.

THE USER'S MANUAL FOR THE ACCOMPANYING DISKS.

Appendices.

Answers to the Exercises.

Index.
�������������������������������������������������
Introduction to Fourier Analysis

M. J. Lighthill

�9.99

January 1958 | Paperback (Hardback) | 80 pages | ISBN: 0521091284

In stock | Stock level updated: 25 May 13:19 BST

This monograph on generalised functions, Fourier integrals and
Fourier series is intended for readers who, while accepting that a
theory where each point is proved is better than one based on
conjecture, nevertheless seek a treatment as elementary and free
from complications as possible. Little detailed knowledge of
particular mathematical techniques is required; the book is
suitable for advanced university students, and can be used as the
basis of a short undergraduate lecture course. A valuable and
original feature of the book is the use of generalised-function
theory to derive a simple, widely applicable method of obtaining
asymptotic expressions for Fourier transforms and Fourier
coefficients. Reviews

'An extremely lucid and well-written account � a stimulating and
valuable addition to the literature of applied mathematics, with a
good deal of the charm of eighteenth-century mathematics. It may
well become a minor classic before very long.'George Weiss,
Science

'Clearly and attractively written, but without any deviation from
rigorous standards of mathematical proof � the book should be well
within the compass of an honours student in mathematics or
theoretical physics, and they are most strongly urged to buy it
and read it.'Science Progess


    Email friend about this title



� Cambridge University Press 2004
������������������������������������������������������������������������
Fourier Analysis:
An Introduction

Elias M. Stein and Rami Shakarchi
Princeton University Press 2003

Cloth | 2003 | $49.95 / �32.95 | ISBN: 0-691-11384-X
320 pp. | 6 x 9 | 40 line illus.

Shopping Cart | Table of Contents
Chapter 1 [in PDF format]

This first volume, a three-part introduction to the subject, is
intended for students with a beginning knowledge of mathematical
analysis who are motivated to discover the ideas that shape
Fourier analysis. It begins with the simple conviction that
Fourier arrived at in the early nineteenth century when studying
problems in the physical sciences--that an arbitrary function can
be written as an infinite sum of the most basic trigonometric
functions.

The first part implements this idea in terms of notions of
convergence and summability of Fourier series, while highlighting
applications such as the isoperimetric inequality and
equidistribution. The second part deals with the Fourier transform
and its applications to classical partial differential equations
and the Radon transform; a clear introduction to the subject
serves to avoid technical difficulties. The book closes with
Fourier theory for finite abelian groups, which is applied to
prime numbers in arithmetic progression.

In organizing their exposition, the authors have carefully
balanced an emphasis on key conceptual insights against the need
to provide the technical underpinnings of rigorous analysis.
Students of mathematics, physics, engineering and other sciences
will find the theory and applications covered in this volume to be
of real interest.

The Princeton Lectures in Analysis represents a sustained effort
to introduce the core areas of mathematical analysis while also
illustrating the organic unity between them. Numerous examples and
applications throughout its four planned volumes, of which Fourier
Analysis is the first, highlight the far-reaching consequences of
certain ideas in analysis to other fields of mathematics and a
variety of sciences. Stein and Shakarchi move from an introduction
addressing Fourier series and integrals to in-depth considerations
of complex analysis; measure and integration theory, and Hilbert
spaces; and, finally, further topics such as functional analysis,
distributions and elements of probability theory.

Elias M. Stein is Professor of Mathematics at Princeton
University. Rami Shakarchi received his Ph.D. in Mathematics from
Princeton University in 2002.

Table of Contents:

Foreword vii
Preface xi
Chapter 1. The Genesis of Fourier Analysis 1
Chapter 2. Basic Properties of Fourier Series 29
Chapter 3. Convergence of Fourier Series 69
Chapter 4. Some Applications of Fourier Series 100
Chapter 5. The Fourier Transform on R 129
Chapter 6. The Fourier Transform on R d 175
Chapter 7. Finite Fourier Analysis 218
Chapter 8. Dirichlet's Theorem 241
Appendix: Integration 281
Notes and References 299
Bibliography 301
Symbol Glossary 305
��������������������������������������������������������������������������
ntroduction to Fourier Analysis on Euclidean Spaces
by Author: Guido L. Weiss
Author: Elias M. Stein
Author: Eilas M. Stein

Binding: Hardcover, 297 pages
Publisher: Princeton Univ Pr
Published Date: 06/01/1971
List Price: USD $90.00
Weight: 1.35 pounds
ISBN: 069108078X
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Fourier Analysis
by T. W. K�rner (Author)
Cambridge University Press; Reprint edition
(November 9, 1989)

The author has provided a shop window for some of the ideas,
techniques and elegant results of Fourier analysis, and for their
applications. These range from number theory, numerical analysis,
control theory and statistics, to earth science, astronomy, and
electrical engineering. Each application is placed in perspective
with a short essay. The prerequisites are few (the reader with
knowledge of second or third year undergraduate mathematics should
have no difficulty following the text), and the style is lively
and entertaining.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Counterexamples in Analysis
by Bernard R. Gelbaum (Author), John M. H. Olmsted (Author)
# Dover Pubns; (June 4, 2003)
# ISBN: 0486428753

These counterexamples, arranged according to difficulty or sophistication, deal mostly with the part of analysis known as "real variables," starting at the level of calculus. The first half of the book concerns functions of a real variable; topics include the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, uniform convergence, and sets and measure on the real axis. The second half, encompassing higher dimensions, examines functions of two variables, plane sets, area, metric and topological spaces, and function spaces. This volume contains much that will prove suitable for students who have not yet completed a first course in calculus, and ample material of interest to more advanced students of analysis as well as graduate students.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Elements of the Theory of Functions and Functional Analysis
by A. N. Kolmogorov, S. V. Fomin
# Dover Pubns; (February 17, 1999)
# ISBN: 0486406830

Based on the authors� courses and lectures, this two-volume
advanced-level text is now available in a single volume. Topics
include metric and normed spaces, continuous curves in metric
spaces, measure theory, Lebesque interval, Hilbert Space and more.
Each section contains exercises. Lists of symbols, definitions and
theorems. 1957 ed.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Functional Analysis
by Frigyes Riesz (Author), Bela Sz.-Nagy (Author)
# Dover Pubns; Reprint edition (June 1, 1990)
# ISBN: 0486662896


Book Description Classic exposition of modern theories of
differentiation and integration and the principal problems and
methods of handling integral equations and linear functionals and
transformations. Topics include Lebesque and Stieltjes integrals,
Hilbert and Banach spaces, self-adjunct transformations, spectral
theories for linear transformations of general type, much more.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Functional Analysis
by Walter Rudin (Author)
# McGraw-Hill Science/Engineering/Math; 2nd edition (January 1, 1991)
# ISBN: 0070542368

I strongly urge any serious math student to own a copy of both Rudin's Principles ("Baby Rudin") and his Real and Complex Analysis ("Adult Rudin"). The former is absolutely essential- without completely mastering continuity and convergence on the basic metric space topology on R^n, higher math is going to be quite a pain. The second is good because it puts the major ideas of basic analysis- Radon measures, L^p spaces, rudiments of Hilbert and Banach Spaces, differentiation and integration, Fourier and Harmonic Analysis, Holomorphic and meromorphic functions, etc. all in one nice volume, although the problems may be too challenging or tangential to master the material by doing them.

With that said, I don't like this book as much. Perhaps because the problems don't provide great movitation for the theorems- in any event, I would recommend using at least two books to understand functional analysis. One that emphasizes a rigorous approach to the theory involved, and another more applied book that allows you to play with the new tools to solve the problems functional analysis was invented to solve; quantum mechanics, for example.

Reed and Simon is a good book, although I'm sure physicists or physics students would probably complain about it for the same reason I like it- its very mathematically rigorous and has a ton of problems- 30 to 60 on average at the end of each chapter, with only a few digressions into applications into quantum physics or elementary QFT. Get this with some Springer text, like Elements of Functional Analysis.

One more note- Rudin's book is broken up into three parts- one on TVS (Topological vector spaces) that combines topological properties of a space (for example, local convexity or local compactness) with the usual vector-space operations to set the spaces where operators act.

The second section deals with distributions- I regret that one failure of "Adult Rudin" was to emphasize the abstract integral as a linear functional, because this would have helped to make the concept of a distribution more clear.

While the introduction to distributions and their connections to Fourier analysis and differential equations is nice, the text gets bogged down with proofs about convolutions that are highly technical (and make either good practice or a good time for Rudin to actually use, for once, "The details are left to the reader...").

Finally, Rudin introduces operator theory, although it could go much more smoothly- the proofs come off as way too technical, a far cry from the "slickness" his proofs are often accused of being in the graduate analysis text.

All in all, there's some interesting problems to do, but you're not going to understand the applications of Functional Analysis to quantum mechanics or PDE (other than distributions a little), where other, more applied (read: easier) books may give nice problems about applications of Hilbert space methods, such as variational techniques or Fredholm theory.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Counterexamples in Topology
by Lynn Arthur Steen (Author), J. Arthur Seebach (Author)
# Dover Pubns; (September 22, 1995)
# ISBN: 048668735X
Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Over 25 Venn diagrams and charts summarize properties of the examples, while discussions of general methods of construction and change give readers insight into constructing counterexamples. Extensive collection of problems and exercises, correlated with examples.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# A Wavelet Tour of Signal Processing, by St�phane Mallat
# ISBN : 0-12-466606-X
# Academic Press, 1999
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Sobolev spaces
Pure and applied mathematics series
Robert A. Adams , J.F. Fournier
Academic Press 2003
ISBN : 0-12-044143-8
Sobolev Spaces presents an introduction to the theory of Sobolev Spaces and other related spaces of function, also to the imbedding characteristics of these spaces. This theory is widely used in pure and Applied Mathematics and in the Physical Sciences.

This second edition of Adam's 'classic' reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike.
Contents

    * Preliminaries
    * The Lebesgue spaces Lp(&#937)
    * The Sobolev spaces W m,p(&#937),
    * The Sobole imbedding theorem
    * Interpolation, extension and approximation theorems
    * Compact imbedding of Sobolev spaces
    * Fractionnal order spaces
    * Orlicz spaces and Orlicz-Sobolev spaces
    * References
    * Index
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    Elliptic Partial Differential Equations of Second Order (Classics in Mathematics)
von David Gilbarg, Neil S. Trudinger
 Springer Verlag 2001
ISBN: 3540411607
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
51.12 VAU   Vauthier-Prat   Cours d'analyse de l'agr�gation


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    Zeidler     Functional analysis
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        Young   An introduction to Hilbert spaces
        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
            Yosida Kosaku   Functional analysis
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    Tisseron Claude     Notions de topologie introduction aux espaces fonctionnels      Hermann     1985
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    Stoyakov    Counter-examples in probability
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    Williams Probability with martingales Oxford
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        Malliavin Paul      Int�gration et probabilites, analyse de Fourier et analyse spectrale    Masson 1982
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    Kahane      S�ries de Fourier al�atoires
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Heuser      Functional Analysis
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Gramain Andre   Int�gration     Hermann     1988
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    Gonnord et Tosel    Topologie et Analyse fonctionnelle      Ellipses    1996
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    Edwards     Functional Analysis

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    Bourbaki, Topologie g�n�rale, chapitres 1 � 4 et 5 � 10, Hermann

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    Cours d'analyse

Th�orie des distributions et analyse de Fourier



Jean-Michel Bony

Les �ditions de l'�cole polytechnique
    * Introduction

    * L'int�grale de Lebesgue
    * Topologie g�n�rale et espaces fonctionnels
    * Fonctions diff�rentiables et approximation
    * Les distributions
    * Op�rations sur les distributions
    * Espaces particuliers de distributions
    * Convolution
    * Quelques �quations de la physique math�matique
    * Transformation de Fourier
    * Espaces de Sobolev

    * Appendices
    * Bibliographie
    * Index
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Analyse de Fourier et applications  - Filtrage, calcul num�rique, ondelettes
Claude Gasquet  Patrick Witomski
Dunod ;  broch� ; scolaire / universitaire  ; 12/2003

Analyse de Fourier et applications  - Exercices corrig�s Edition 2000
Robert Dalmasso  Patrick Witomski
Dunod ;  broch� ; manuel  ; 02/2000
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
#

@book {Jaffard01wavelets,
AUTHOR = {Jaffard, St{\'e}phane and Meyer, Yves and Ryan, Robert D.},
TITLE = {Wavelets},
EDITION = {Revised},
NOTE = {Tools for science and technology},
PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)},
ADDRESS = {Philadelphia, PA},
YEAR = {2001},
PAGES = {xiv+256},
ISBN = {0-89871-448-6},
MRCLASS = {00A69 (42-02 42C40 94A08 94A12)},
MRNUMBER = {2002g:00007},
MRREVIEWER = {Peter A. McCoy},

}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# Yves Meyer. Wavelets. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1993.
Note: Algorithms & applications, Translated from the French and with a foreword by Robert D. Ryan.

@book {Meyer93wavelets,
AUTHOR = {Meyer, Yves},
TITLE = {Wavelets},
NOTE = {Algorithms \& applications, Translated from the French and with a foreword by Robert D. Ryan},
PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)},
ADDRESS = {Philadelphia, PA},
YEAR = {1993},
PAGES = {xii+133},
ISBN = {0-89871-309-9},
MRCLASS = {94A12 (00A69 42C15 68U10 94A11)},
MRNUMBER = {95f:94005},
MRREVIEWER = {Peter A. McCoy},

}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
