Mathematical Foundations for Computer Vision, Machine Learning, and Robotics - Volume 2: Aspects of Representation Theory and Noncommutative Harmonic Analysis - Hardcover

Gallier, Jean; Quaintance, Jocelyn

Hardcover

ISBN 10: 9819810817 ISBN 13: 9789819810819

Publisher: World Scientific Publishing, 2025

Synopsis

This book presents the theory of harmonic analysis for noncommutative compact groups. If G is a commutative locally compact group, there is a well-understood theory of harmonic analysis as discussed in Aspects of Harmonic Analysis on Locally Compact Abelian Groups. If G is not commutative, things are a lot tougher. In the special case of a compact group, there is a deep interplay between analysis and representation theory which was first discovered by Hermann Weyl and refined by Andre Weil. This book presents these seminal results of Weyl and Weil. Starting with the basics of representations theory, it presents the famous Peter–Weyl theorems and discusses Fourier analysis on compact groups. This book also introduces the reader to induced representations of locally compact groups, induced representations of G-bundles, and the theory of Gelfand pairs. A special feature is the chapter on equivariant convolutional neural networks (CNNs), a chapter which shows how many of the abstract concepts of representations, analysis on compact groups, Peter–Weyl theorems, Fourier transform, induced representations are used to tackle very practical, modern-day problems.

About this title

About the Authors

Professor Jean Gallier has been with the University of Pennsylvania's Computer and Information Science Department for over 40 years. He holds a PhD in computer science from UCLA and is a world-renowned expert in computational logic. He also holds a joint appointment from the University of Pennsylvania's Department of Mathematics. Besides his seminal work on Horn satisfiability, he is known for his mathematical textbooks on geometric modeling, linear algebra, and differential geometry. He is the author of 12 books, a listing of which can be found at https://www.cis.upenn.edu/~jean/home.html.

Jocelyn Quaintance is a lecturer at the University of Pennsylvania's Computer and Information Science Department who specializes in linear algebra instruction for the online Masters of Computer and Information Technology degree. She holds a PhD in mathematics from the University of Pittsburgh. She is known for her research in combinatorial identities and power product expansions and has over 30 peer-reviewed publications. She is also known for her textbooks, which combine mathematical theory with computer science applications. Along with her co-author Jean Gallier, she has published books on linear algebra, differential geometry, cohomology, and harmonic analysis.

Edition details

• Publisher: World Scientific Publishing
• Publication date: 2025
• Language: English
• ISBN 10: 9819810817
• ISBN 13: 9789819810819
• Binding: Hardcover
• Number of pages: 768