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Fourier Analysis on Polytopes and the Geometry of Numbers: Part I: A Friendly Introduction
 
Sinai Robins University of São Paulo, São Paulo, Brazil
Softcover ISBN:  978-1-4704-7033-3
Product Code:  STML/107
List Price: $59.00
Individual Price: $47.20
MAA Member Price: $47.20
Not yet published - Preorder Now!
Expected availability date: June 06, 2024
eBook ISBN:  978-1-4704-7663-2
Product Code:  STML/107.E
List Price: $59.00
Individual Price: $47.20
MAA Member Price: $47.20
Softcover ISBN:  978-1-4704-7033-3
eBook: ISBN:  978-1-4704-7663-2
Product Code:  STML/107.B
List Price: $118.00 $88.50
MAA Member Price: $94.40 $70.80
Not yet published - Preorder Now!
Expected availability date: April 17, 2024
Click above image for expanded view
Fourier Analysis on Polytopes and the Geometry of Numbers: Part I: A Friendly Introduction
Sinai Robins University of São Paulo, São Paulo, Brazil
Softcover ISBN:  978-1-4704-7033-3
Product Code:  STML/107
List Price: $59.00
Individual Price: $47.20
MAA Member Price: $47.20
Not yet published - Preorder Now!
Expected availability date: June 06, 2024
eBook ISBN:  978-1-4704-7663-2
Product Code:  STML/107.E
List Price: $59.00
Individual Price: $47.20
MAA Member Price: $47.20
Softcover ISBN:  978-1-4704-7033-3
eBook ISBN:  978-1-4704-7663-2
Product Code:  STML/107.B
List Price: $118.00 $88.50
MAA Member Price: $94.40 $70.80
Not yet published - Preorder Now!
Expected availability date: April 17, 2024
  • Book Details
     
     
    Student Mathematical Library
    Volume: 1072024; 325 pp
    MSC: Primary 51; 11; 32; 52

    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.

    Readership

    Undergraduate and graduate students and researchers interested in analysis and periodical structures.

  • Table of Contents
     
     
    • Chapters
    • 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
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 1072024; 325 pp
MSC: Primary 51; 11; 32; 52

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.

Readership

Undergraduate and graduate students and researchers interested in analysis and periodical structures.

  • Chapters
  • 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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