Coverart for item
The Resource Fourier analysis on finite Abelian groups, Bao Luong

Fourier analysis on finite Abelian groups, Bao Luong

Label
Fourier analysis on finite Abelian groups
Title
Fourier analysis on finite Abelian groups
Statement of responsibility
Bao Luong
Creator
Subject
Language
eng
Summary
Fourier analysis has been the inspiration for a technological wave of advances in fields such as imaging processing, financial modeling, cryptography, algorithms, and sequence design. This self-contained book provides a thorough look at the Fourier transform, one of the most useful tools in applied mathematics. With countless examples and unique exercise sets at the end of most sections, Fourier Analysis on Finite Abelian Groups is a perfect companion for a first course in Fourier analysis. The first two chapters provide fundamental material for a strong foundation to deal with subsequent chapters. Special topics covered include: * Computing eigenvalues of the Fourier transform * Applications to Banach algebras * Tensor decompositions of the Fourier transform * Quadratic Gaussian sums This book provides a useful introduction for well-prepared undergraduate and graduate students and powerful applications that may appeal to researchers and mathematicians. The only prerequisites are courses in group theory and linear algebra
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Luong, Bao
Dewey number
515/.2433
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA403.5
LC item number
.L86 2009
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Applied and numerical harmonic analysis
http://library.link/vocab/subjectName
  • Fourier analysis
  • Abelian groups
  • Finite groups
  • Abelian groups
  • Finite groups
  • Fourier analysis
  • Fourier-Transformation
Label
Fourier analysis on finite Abelian groups, Bao Luong
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface -- Overview -- Chapter 1: Foundation Material -- Results from Group Theory -- Quadratic Congruences -- Chebyshev Systems of Functions -- Chapter 2: The Fourier Transform -- A Special Class of Linear Operators -- Characters -- The Orthogonal Relations for Characters -- The Fourier Transform -- The Fourier Transform of Periodic Functions -- The Inverse Fourier Transform -- The Inversion Formula -- Matrices of the Fourier Transform -- Iterated Fourier Transform -- Is the Fourier Transform a Self-Adjoint Operator? -- The Convolutions Operator -- Banach Algebra -- The Uncertainty Principle -- The Tensor Decomposition -- The Tensor Decomposition of Vector Spaces -- The Fourier Transform and Isometries -- Reduction to Finite Cyclic Groups -- Symmetric and Antisymmetric Functions -- Eigenvalues and Eigenvectors -- Spectrak Theorem -- Ergodic Theorem -- Multiplicities of Eigenvalues -- The Quantum Fourier Transform -- Chapter 3: Quadratic Sums -- 1. The Number G_n(1) -- Reduction Formulas
Control code
656399104
Dimensions
unknown
Extent
1 online resource (xvi, 156 pages)
Form of item
online
Isbn
9780817649166
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-0-8176-4916-6
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-0-8176-4915-9
Publisher number
12548750
Specific material designation
remote
System control number
(OCoLC)656399104
Label
Fourier analysis on finite Abelian groups, Bao Luong
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface -- Overview -- Chapter 1: Foundation Material -- Results from Group Theory -- Quadratic Congruences -- Chebyshev Systems of Functions -- Chapter 2: The Fourier Transform -- A Special Class of Linear Operators -- Characters -- The Orthogonal Relations for Characters -- The Fourier Transform -- The Fourier Transform of Periodic Functions -- The Inverse Fourier Transform -- The Inversion Formula -- Matrices of the Fourier Transform -- Iterated Fourier Transform -- Is the Fourier Transform a Self-Adjoint Operator? -- The Convolutions Operator -- Banach Algebra -- The Uncertainty Principle -- The Tensor Decomposition -- The Tensor Decomposition of Vector Spaces -- The Fourier Transform and Isometries -- Reduction to Finite Cyclic Groups -- Symmetric and Antisymmetric Functions -- Eigenvalues and Eigenvectors -- Spectrak Theorem -- Ergodic Theorem -- Multiplicities of Eigenvalues -- The Quantum Fourier Transform -- Chapter 3: Quadratic Sums -- 1. The Number G_n(1) -- Reduction Formulas
Control code
656399104
Dimensions
unknown
Extent
1 online resource (xvi, 156 pages)
Form of item
online
Isbn
9780817649166
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-0-8176-4916-6
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-0-8176-4915-9
Publisher number
12548750
Specific material designation
remote
System control number
(OCoLC)656399104

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