Fourier Analysis on Finite Groups and Applications: A Gateway to Symmetry and Its Transformative Power

Symmetry, an inherent property of nature, plays a pivotal role in countless scientific and engineering disciplines. Fourier analysis, a powerful mathematical tool, provides a framework to analyze and manipulate symmetry-related phenomena. When combined with the theory of finite groups, Fourier analysis offers an unparalleled lens to study the intricate patterns and symmetries that govern the behavior of matter and information. This book, "Fourier Analysis on Finite Groups and Applications," serves as a comprehensive guide to this captivating field.

Fourier Analysis on Finite Groups and Applications (London Mathematical Society Student Texts Book 43)

by Audrey Terras

4.2 out of 5

Language	:	English
File size	:	20373 KB
Print length	:	456 pages
Screen Reader	:	Supported

FREE

Overview of the Book

This remarkable book is a comprehensive treatise that meticulously explores the fundamental concepts and techniques of Fourier analysis on finite groups. Authored by the esteemed Professor Bruce Bartlett, a renowned expert in the field, this book presents a detailed exposition of the subject, making it accessible to both novice and seasoned researchers alike.

The book is meticulously structured into six chapters, each delving into a specific aspect of Fourier analysis on finite groups. The initial chapters lay the groundwork by introducing the fundamental concepts of Fourier analysis and finite group theory. Subsequent chapters delve into more advanced topics, such as representation theory, the Peter-Weyl theorem, and applications in quantum computing and image processing.

Key Concepts and Techniques

Fourier analysis on finite groups revolves around the concept of the Fourier transform, which decomposes a function or signal into its constituent frequencies. This transformative tool allows for the analysis and manipulation of signals and functions in the frequency domain. The book meticulously explains the theory behind the Fourier transform and its application to finite groups.

The study of finite groups and their representations provides a deeper understanding of symmetry and its manifestations. The book introduces the fundamental concepts of group theory and develops the theory of group representations. These concepts are essential for understanding the structure of finite groups and their symmetries.

Applications in Diverse Fields

Fourier analysis on finite groups has found groundbreaking applications in a wide range of disciplines, including mathematics, physics, and computer science. This book explores some of these applications, demonstrating the transformative power of Fourier analysis in:

• Quantum Computing: Fourier analysis plays a crucial role in quantum computing algorithms, enabling efficient manipulation of quantum information.
• Image Processing: Fourier analysis is essential for image processing techniques such as image enhancement, denoising, and feature extraction.
• Crystallography: The analysis of crystal structures relies heavily on Fourier analysis to determine the arrangement of atoms and molecules in crystals.

Educational Value and Significance

This book is not merely a theoretical treatise; it is a pedagogical masterpiece designed to facilitate a profound understanding of Fourier analysis on finite groups. Each chapter is meticulously structured with clear explanations, detailed examples, and thought-provoking exercises. This structured approach caters to students and researchers from a wide range of backgrounds, empowering them to delve into this fascinating field.

The book is an invaluable resource for graduate students and researchers in mathematics, physics, and computer science. It provides a comprehensive foundation for further research and exploration in the field of Fourier analysis on finite groups and its applications. Moreover, it serves as an excellent reference for practitioners seeking to apply these concepts to real-world problems.

"Fourier Analysis on Finite Groups and Applications" is an essential resource for anyone seeking to master the intricate world of Fourier analysis on finite groups. Its comprehensive approach, meticulous explanations, and wide-ranging applications make it a must-have for students, researchers, and practitioners alike. Through this book, readers embark on a captivating journey to unveil the hidden symmetries and patterns that shape the world around us.

Fourier Analysis on Finite Groups and Applications (London Mathematical Society Student Texts Book 43)

by Audrey Terras

4.2 out of 5

Language	:	English
File size	:	20373 KB
Print length	:	456 pages
Screen Reader	:	Supported

FREE