Shortcuts
Top of page (Alt+0)
Page content (Alt+9)
Page menu (Alt+8)
Your browser does not support javascript, some WebOpac functionallity will not be available.
.
Default
.
PageMenu
-
Main Menu
-
Simple Search
.
Advanced Search
.
Journal Search
.
Refine Search Results
.
Preferences
.
Search Menu
Simple Search
.
Advanced Search
.
New Items Search
.
Journal Search
.
Refine Search Results
.
Bottom Menu
Help
Italian
.
English
.
German
.
New Item Menu
New Items Search
.
New Items List
.
Links
SISSA Library
.
ICTP library
.
Italian National web catalog (SBN)
.
Trieste University web catalog
.
Udine University web catalog
.
© LIBERO v6.4.1sp220816
Page content
You are here
:
Catalogue Display
Catalogue Display
Fourier Series: A Modern Introduction Volume 1
.
Bookmark this Record
Catalogue Record 44291
.
.
Author info on Wikipedia
.
.
LibraryThing
.
.
Google Books
.
.
Amazon Books
.
Catalogue Information
Catalogue Record 44291
.
Reviews
Catalogue Record 44291
.
British Library
Resolver for RSN-44291
Google Scholar
Resolver for RSN-44291
WorldCat
Resolver for RSN-44291
Catalogo Nazionale SBN
Resolver for RSN-44291
GoogleBooks
Resolver for RSN-44291
ICTP Library
Resolver for RSN-44291
.
Share Link
Jump to link
Catalogue Information
Field name
Details
Dewey Class
515.8
Title
Fourier Series ([EBook]) : A Modern Introduction Volume 1 / by R. E. Edwards.
Author
Edwards, Robert E. , 1926-
Other name(s)
SpringerLink (Online service)
Edition statement
Second Edition.
Publication
New York, NY : Springer , 1979.
Physical Details
XII, 228 pages : online resource.
Series
Graduate texts in mathematics
0072-5285 ; ; 64
ISBN
9781461262084
Summary Note
The principal aim in writing this book has been to provide an intro duction, barely more, to some aspects of Fourier series and related topics in which a liberal use is made of modem techniques and which guides the reader toward some of the problems of current interest in harmonic analysis generally. The use of modem concepts and techniques is, in fact, as wide spread as is deemed to be compatible with the desire that the book shall be useful to senior undergraduates and beginning graduate students, for whom it may perhaps serve as preparation for Rudin's Harmonic Analysis on Groups and the promised second volume of Hewitt and Ross's Abstract Harmonic Analysis. The emphasis on modem techniques and outlook has affected not only the type of arguments favored, but also to a considerable extent the choice of material. Above all, it has led to a minimal treatment of pointwise con vergence and summability: as is argued in Chapter 1, Fourier series are not necessarily seen in their best or most natural role through pointwise-tinted spectacles. Moreover, the famous treatises by Zygmund and by Baryon trigonometric series cover these aspects in great detail, wl:tile leaving some gaps in the presentation of the modern viewpoint; the same is true of the more elementary account given by Tolstov. Likewise, and again for reasons discussed in Chapter 1, trigonometric series in general form no part of the program attempted.:
Contents note
Contentss -- 1 Trigonometric Series and Fourier Series -- 1.1 The Genesis of Trigonometric Series and Fourier Series -- 1.2 Pointwise Representation of Functions by Trigonometric Series -- 1.3 New Ideas about Representation -- Exercises -- 2 Group Structure and Fourier Series -- 2.1 Periodic Functions -- 2.2 Translates of Functions. Characters and Exponentials. The Invariant Integral -- 2.3 Fourier Coefficients and Their Elementary Properties -- 2.4 The Uniqueness Theorem and the Density of Trigonometric Polynomials -- 2.5 Remarks on the Dual Problems -- Exercises -- 3 Convolutions of Functions -- 3.1 Definition and First Properties of Convolution -- 3.2 Approximate Identities for Convolution -- 3.3 The Group Algebra Concept -- 3.4 The Dual Concepts -- Exercises -- 4 Homomorphisms of Convolution Algebras -- 4.1 Complex Homomorphisms and Fourier Coefficients -- 4.2 Homomorphisms of the Group Algebra -- Exercises -- 5 The Dirichlet and Fejér Kernels. Cesàro Summability -- 5.1 The Dirichlet and Fejér Kernels -- 5.2 The Localization Principle -- 5.3 Remarks concerning Summability -- Exercises -- 6 Cesàro Summability of Fourier Series and its Consequences -- 6.1 Uniform and Mean Summability -- 6.2 Applications and Corollaries of.1.1 90 -- 6.3 More about Pointwise Summability -- 6.4 Pointwise Summability Almost Everywhere -- 6.5 Approximation by Trigonometric Polynomials -- 6.6 General Comments on Summability of Fourier Series -- 6.7 Remarks on the Dual Aspects -- Exercises -- 7 Some Special Series and Their Applications -- 7.1 Some Preliminaries -- 7.2 Pointwise Convergence of the Series (C) and (S) -- 7.3 The Series (C) and (S) as Fourier Series -- 7.4 Application to A(Z) -- 7.5 Application to Factorization Problems -- Exercises -- 8 Fourier Series in L2 -- 8.1 A Minimal Property -- 8.2 Mean Convergence of Fourier Series in L2. Parseval’s Formula -- 8.3 The Riesz-Fischer Theorem -- 8.4 Factorization Problems Again -- 8.5 More about Mean Moduli of Continuity -- 8.6 Concerning Subsequences of sNf -- 8.7 A(Z) Once Again -- Exercises -- 9 Positive Definite Functions and Bochner’s Theorem -- 9.1 Mise-en-Scène -- 9.2 Toward the Bochner Theorem -- 9.3 An Alternative Proof of the Parseval Formula -- 9.4 Other Versions of the Bochner Theorem -- Exercises -- 10 Pointwise Convergence of Fourier Series -- 10.1 Functions of Bounded Variation and Jordan’s Test -- 10.2 Remarks on Other Criteria for Convergence; Dini’s Test -- 10.3 The Divergence of Fourier Series -- 10.4 The Order of Magnitude of sNf. Pointwise Convergence Almost Everywhere -- 10.5 More about the Parseval Formula -- 10.6 Functions with Absolutely Convergent Fourier Series -- Exercises -- Appendix A Metric Spaces and Baire’s Theorem -- A.1 Some Definitions -- A.2 Baire’s Category Theorem -- A.3 Corollary -- A.4 Lower Semicontinuous Functions -- A.5 A Lemma -- Appendix B Concerning Topological Linear Spaces -- B.1 Preliminary Definitions -- B.2 Uniform Boundedness Principles -- B.3 Open Mapping and Closed Graph Theorems -- B.4 The Weak Compacity Principle -- B.5 The Hahn-Banach Theorem -- Appendix D A WEAK FORM OF RUNGE’S THEOREM -- Research Publications -- Symbols.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-1-4612-6208-4
Links to Related Works
Subject References:
Functions of real variables
.
Mathematics
.
Real Functions
.
Authors:
Edwards, Robert E. 1926-
.
Corporate Authors:
SpringerLink (Online service)
.
Series:
Graduate texts in mathematics
.
GTM
.
Classification:
515.8
.
.
ISBD Display
Catalogue Record 44291
.
Tag Display
Catalogue Record 44291
.
Related Works
Catalogue Record 44291
.
Marc XML
Catalogue Record 44291
.
Add Title to Basket
Catalogue Record 44291
.
Catalogue Information 44291
Beginning of record
.
Catalogue Information 44291
Top of page
.
Download Title
Catalogue Record 44291
Export
This Record
As
Labelled Format
Bibliographic Format
ISBD Format
MARC Format
MARC Binary Format
MARCXML Format
User-Defined Format:
Title
Author
Series
Publication Details
Subject
To
File
Email
Reviews
This item has not been rated.
Add a Review and/or Rating
44291
1
44291
-
2
44291
-
3
44291
-
4
44291
-
5
44291
-
Quick Search
Search for