ENGLISH

Aspects of Harmonic Analysis on Locally Compact Abelian Groups

By Jean Gallier , Jocelyn Quaintance

Book information

Publisher
World Scientific
Year
2024
ISBN
9789811291715, 9789811291739
DOI
10.1142/13799
Language
english
Format
DJVU
Filesize
9 MB (9870784 bytes)
Series
Mathematical Foundations for Computer Vision, Machine Learning, and Robotics 1
Edition
1
Pages
747\760
Topic
Mathematics\\Analysis
DPI
400
Orientation
yes
Paginated
no
Scanned
portrait
Time added
2024-09-15 16:30:31
Bochner IntegralFourier TransformHaar Measureharmonic analysisLocally Compact Abelian GroupsMeasure TheoryNormed AlgebrasRadon Functionals

Description

The Fourier transform is a "tool" used in engineering and computer vision to model periodic phenomena. Starting with the basics of measure theory and integration, this book delves into the harmonic analysis of locally compact abelian groups. It provides an in-depth tour of the beautiful theory of the Fourier transform based on the results of Gelfand, Pontrjagin, and Andre Weil in a manner accessible to an undergraduate student who has taken linear algebra and introductory real analysis. Highlights of this book include the Bochner integral, the Haar measure, Radon functionals, the theory of Fourier analysis on the circle, and the theory of the discrete Fourier transform. After studying this book, the reader will have the preparation necessary for understanding the Peter–Weyl theorems for complete, separable Hilbert algebras, a key theoretical concept used in the construction of Gelfand pairs and equivariant convolutional neural networks.

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