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interface between convex geometry and harmonic analysis - Info and Reading Options

"interface between convex geometry and harmonic analysis" is published by American Mathematical Society in c2008 - Rhode Island, the book is classified in bibliography genre and the language of the book is English.


“interface between convex geometry and harmonic analysis” Metadata:

  • Title: ➤  interface between convex geometry and harmonic analysis
  • Authors: ➤  
  • Language: English
  • Publisher: American Mathematical Society
  • Publish Date:
  • Publish Location: Rhode Island
  • Genres: ➤  bibliography - conference publication - Conference papers and proceedings - Congresses
  • Dewey Decimal Classification: 516/.08
  • Library of Congress Classification: QA639.5 .K64 2008

“interface between convex geometry and harmonic analysis” Subjects and Themes:

Edition Specifications:

  • Number of Pages: x, 107 p. : ill. ; 26 cm.

Edition Identifiers:

AI-generated Review of “interface between convex geometry and harmonic analysis”:


"interface between convex geometry and harmonic analysis" Table Of Contents:

  • 1- Hyperplane sections of lp
  • 2- alls
  • 3- 1.1. Lecture 1
  • 4- Volume and the Fourier transform
  • 5- 2.1. Lecture 2
  • 6- Intersection bodies
  • 7- 3.1. Lecture 3
  • 8- 3.2. Intersection bodies and ellipsoids
  • 9- 3.3. Non
  • 10- ntersection bodies all of whose central sections are intersection bodies
  • 11- 3.4. Generalized intersection bodies
  • 12- The Busemann
  • 13- etty problem
  • 14- 4.1. Lecture 4
  • 15- 4.2. A modification of the Busemann
  • 16- etty problem
  • 17- 4.3. The Busemann
  • 18- etty problem in hyperbolic and spherical spaces
  • 19- 4.4. The lower dimensional Busemann
  • 20- etty problem
  • 21- Projections and the Fourier transform
  • 22- 5.1. Lecture 5
  • 23- Intersection bodies and Lp
  • 24- paces
  • 25- 6.1. Lecture 6
  • 26- On the road between polar projection bodies and intersection bodies
  • 27- 7.1. Lecture 7
  • 28- 7.2. The geometry of L0
  • 29- 7.3. A Banach subspace of L1/2 that does not embed in L1
  • 30- 7.4. Common subspaces of Lp spaces
  • 31- Open problems.

"interface between convex geometry and harmonic analysis" Description:

Harvard Library:

"The study of convex bodies is a central part of geometry, and is particularly useful in applications to other areas of mathematics and the sciences. Recently, methods from Fourier analysis have been developed that greatly improve our understanding of the geometry of sections and projections of convex bodies. The idea of this approach is to express certain properties of bodies in terms of the Fourier transform and then to use methods of Fourier analysis to solve geometric problems. The results covered in the book include an analytic solution to the Busemann-Petty problem, which asks whether bodies with smaller areas of central hyperplane sections necessarily have smaller volume, characterizations of intersection bodies, extremal sections of certain classes of bodies, and a Fourier analytic solution to Shephard's problem on projections of convex bodies." "The book is written in the form of lectures accessible to graduate students. This approach allows the reader to clearly see the main ideas behind the method, rather than to dwell on technical difficulties. The book also contains discussions of the most recent advances in the subject. The first section of each lecture is a snapshot of that lecture. By reading each of these sections first, novices can gain an overview of the subject, then return to the full text for more details."--Jacket.

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