Discrete Harmonic Analysis: Representations, Number Theory, Expanders, and the Fourier Transform

This comprehensive work delves into discrete harmonic analysis, weaving together a variety of mathematical concepts and theories. The authors, Tullio Ceccherini-Silberstein, Fabio Scarabotti, and Filippo Tolli, meticulously explore the relationship between harmonic analysis and number theory, providing readers with a deep understanding of the foundational principles that govern these disciplines.

Through clear explanations and engaging examples, the book highlights the significance of representations and their applications in modern mathematics. It also examines expanders and their role in discrete systems, showcasing their relevance in various practical and theoretical contexts. The Fourier transform emerges as a critical tool throughout the text, connecting the mathematical theories with real-world applications.

Readers will appreciate the self-contained nature of the material, which facilitates learning for both advanced students and seasoned mathematicians. The emphasis on discrete harmonic analysis presents an innovative perspective, making this work a valuable contribution to the field and an essential resource for those looking to deepen their knowledge in this area of study.