Fourier Analysis on Polytopes and the Geometry of Numbers

Download or read book Fourier Analysis on Polytopes and the Geometry of Numbers written by Sinai Robins and published by American Mathematical Society. This book was released on 2024-04-24 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 interested in exploring this important expanding field.