Fourier Analysis on Polytopes and the Geometry of Numbers: Part I: A Friendly Introduction
Author:   Sinai Robins
Publisher:   American Mathematical Society
Volume:   107
ISBN:  

9781470470333


Pages:   349
Publication Date:   31 May 2024
Format:   Paperback
Availability:   In Print   Availability explained
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Fourier Analysis on Polytopes and the Geometry of Numbers: Part I: A Friendly Introduction


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Overview

This book offers a gentle introduction to the geometry of numbers from a modern Fourier-analytic point of view. One of the main themes is the transfer of geometric knowledge of a polytope to analytic knowledge of its Fourier transform. The Fourier transform preserves all of the information of a polytope, and turns its geometry into analysis. The approach is unique, and streamlines this emerging field by presenting new simple proofs of some basic results of the field. In addition, each chapter is fitted with many exercises, some of which have solutions and hints in an appendix. Thus, an individual learner will have an easier time absorbing the material on their own, or as part of a class. Overall, this book provides an introduction appropriate for an advanced undergraduate, a beginning graduate student, or researcher interesting in exploring this important expanding field.

Full Product Details

Author:   Sinai Robins
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Volume:   107
Weight:   0.184kg
ISBN:  

9781470470333


ISBN 10:   1470470330
Pages:   349
Publication Date:   31 May 2024
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

Motivational problem: Tiling a rectangle with rectangles Examples nourish the theory The basics of Fourier analysis Geometry of numbers, Part I: Minkowski meets Siegel An introduction to Euclidean lattices Geometry of numbers, Part II: Blichfedt's theorem The Fourier transform of a polytope via its vertex description: Brion's theorem What is an angle in higher dimensions? Appendix A. Solutions and hints to selected problems Appendix B. The dominated convergence theorem and other goodies Bibliography Index

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Sinai Robins, University of Sao Paulo, Brazil.

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