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 and Wavelet Analysis
.
Bookmark this Record
Catalogue Record 49209
.
.
Author info on Wikipedia
.
.
LibraryThing
.
.
Google Books
.
.
Amazon Books
.
Catalogue Information
Catalogue Record 49209
.
Reviews
Catalogue Record 49209
.
British Library
Resolver for RSN-49209
Google Scholar
Resolver for RSN-49209
WorldCat
Resolver for RSN-49209
Catalogo Nazionale SBN
Resolver for RSN-49209
GoogleBooks
Resolver for RSN-49209
ICTP Library
Resolver for RSN-49209
.
Share Link
Jump to link
Catalogue Information
Field name
Details
Dewey Class
515.7
Title
Fourier and Wavelet Analysis ([EBook]) / by George Bachman, Lawrence Narici, Edward Beckenstein.
Author
Bachman, George , 1929-
Added Personal Name
Narici, Lawrence
Beckenstein, Edward
Other name(s)
SpringerLink (Online service)
Publication
New York, NY : Springer , 2000.
Physical Details
IX, 507 pages : online resource.
Series
Universitext
0172-5939
ISBN
9781461205050
Summary Note
globalized Fejer's theorem; he showed that the Fourier series for any f E Ld-7I", 7I"] converges (C, 1) to f (t) a.e. The desire to do this was part of the reason that Lebesgue invented his integral; the theorem mentioned above was one of the first uses he made of it (Sec. 4.18). Denjoy, with the same motivation, extended the integral even further. Concurrently, the emerging point of view that things could be decom posed into waves and then reconstituted infused not just mathematics but all of science. It is impossible to quantify the role that this perspective played in the development of the physics of the nineteenth and twentieth centuries, but it was certainly great. Imagine physics without it. We develop the standard features of Fourier analysis-Fourier series, Fourier transform, Fourier sine and cosine transforms. We do NOT do it in the most elegant way. Instead, we develop it for the reader who has never seen them before. We cover more recent developments such as the discrete and fast Fourier transforms and wavelets in Chapters 6 and 7. Our treatment of these topics is strictly introductory, for the novice. (Wavelets for idiots?) To do them properly, especially the applications, would take at least a whole book.:
Contents note
1 Metrie and Normed Spaces -- 1.1 Metrie Spaces -- 1.2 Normed Spaces -- 1.3 Inner Product Spaces -- 1.4 Orthogonality -- 1.5 Linear Isometry -- 1.6 Holder and Minkowski Inequalities; Lpand lpSpaces. -- 2 Analysis -- 2.1 Balls -- 2.2 Convergence and Continuity -- 2.3 Bounded Sets -- 2.4 Closure and Closed Sets -- 2.5 Open Sets -- 2.6 Completeness -- 2.7 Uniform Continuity -- 2.8 Compactness -- 2.9 Equivalent Norms -- 2.10 Direct Sums -- 3 Bases -- 3.1 Best Approximation -- 3.2 Orthogonal Complements and the Projection Theorem -- 3.3 Orthonormal Sequences -- 3.4 Orthonormal Bases -- 3.5 The Haar Basis -- 3.6 Unconditional Convergence -- 3.7 Orthogonal Direct Sums -- 3.8 Continuous Linear Maps -- 3.9 Dual Spaces -- 3.10 Adjoints -- 4 Fourier Series -- 4.1 Warmup -- 4.2 Fourier Sine Series and Cosine Series -- 4.3 Smoothness -- 4.4 The Riemann-Lebesgue Lemma -- 4.5 The Dirichlet and Fourier Kernels -- 4.6 Point wise Convergence of Fourier Series -- 4.7 Uniform Convergence -- 4.8 The Gibbs Phenomenon -- 4.9 — Divergent Fourier Series -- 4.10 Termwise Integration -- 4.11 Trigonometric vs. Fourier Series -- 4.12 Termwise Differentiation -- 4.13 Dido’s Dilemma -- 4.14 Other Kinds of Summability -- 4.15 Fejer Theory -- 4.16 The Smoothing Effect of (C, 1) Summation -- 4.17 Weierstrass’s Approximation Theorem -- 4.18 Lebesgue’s Pointwise Convergence Theorem -- 4.19 Higher Dimensions -- 4.20 Convergence of Multiple Series -- 5 The Fourier Transform -- 5.1 The Finite Fourier Transform -- 5.2 Convolution on T -- 5.3 The Exponential Form of Lebesgue’s Theorem -- 5.4 Motivation and Definition -- 5.5 Basics/Examplesv -- 5.6 The Fourier Transform and Residues -- 5.7 The Fourier Map -- 5.8 Convolution on R -- 5.9 Inversion, Exponential Form -- 5.10 Inversion, Trigonometric Form -- 5.11 (C, 1) Summability for Integrals -- 5.12 The Fejer-Lebesgue Inversion Theorem -- 5.13 Convergence Assistance -- 5.14 Approximate Identity -- 5.15 Transforms of Derivatives and Integrals -- 5.16 Fourier Sine and Cosine Transforms -- 5.17 Parseval’s Identities -- 5.18 The L2Theory -- 5.19 The Plancherel Theorem -- 5.20 Point wise Inversion and Summability -- 5.21 — Sampling Theorem -- 5.22 The Mellin Transform -- 5.23 Variations -- 6 The Discrete and Fast Fourier Transforms -- 6.1 The Discrete Fourier Transform -- 6.2 The Inversion Theorem for the DFT -- 6.3 Cyclic Convolution -- 6.4 Fast Fourier Transform for N=2k -- 6.5 The Fast Fourier Transform for N=RC -- 7 Wavelets -- 7.1 Orthonormal Basis from One Function -- 7.2 Multiresolution Analysis -- 7.3 Mother Wavelets Yield Wavelet Bases -- 7.4 From MRA to Mother Wavelet -- 7.5 Construction of — Scaling Function with Compact Support -- 7.6 Shannon Wavelets -- 7.7 Riesz Bases and MRAs -- 7.8 Franklin Wavelets -- 7.9 Frames -- 7.10 Splines -- 7.11 The Continuous Wavelet Transform.
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/10.1007/978-1-4612-0505-0
Links to Related Works
Subject References:
Analysis
.
Analysis (Mathematics)
.
Functional Analysis
.
Lie groups
.
Mathematical analysis
.
Mathematics
.
Topological groups
.
Topological groups, Lie groups
.
Authors:
author
.
Bachman, George 1929-
.
Beckenstein, Edward
.
Bachman, George, 1929-
.
Narici, Lawrence
.
Corporate Authors:
SpringerLink (Online service)
.
Series:
Universitext
.
Classification:
515.7
.
.
ISBD Display
Catalogue Record 49209
.
Tag Display
Catalogue Record 49209
.
Related Works
Catalogue Record 49209
.
Marc XML
Catalogue Record 49209
.
Add Title to Basket
Catalogue Record 49209
.
Catalogue Information 49209
Beginning of record
.
Catalogue Information 49209
Top of page
.
Download Title
Catalogue Record 49209
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
49209
1
49209
-
2
49209
-
3
49209
-
4
49209
-
5
49209
-
Quick Search
Search for