凸几何中的Fourier分析（影印版）

样章

作者：

Alexander Koldobsky

定价：

99.00元

版面字数：

430.00千字

开本：

16开

装帧形式：

精装

版次：

最新版次
印刷时间：

2026-01-09

ISBN：

978-7-04-066135-4

物料号：

66135-00

出版时间：

2026-03-27

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

分析

暂无

前辅文
Chapter 1. Introduction
Chapter 2. Basic Concepts
- 2.1. Star bodies
- 2.2. Convex bodies
- 2.3. Radon transforms
- 2.4. The Gamma-function
- 2.5. The Fourier transform of distributions
- 2.6. Fractional derivatives
- 2.7. Positive definite distributions
- 2.8. Stable random variables and the function γq
Chapter 3. Volume and the Fourier Transform
- 3.1. The first examples: hyperplane sections of ℓq-balls
- 3.2. A general formula for the volume of hyperplane sections
- 3.3. The parallel section function and the Fourier transform
- 3.4. Parseval's formula on the sphere
- 3.5. Remarks and further results
Chapter 4. Intersection Bodies
- 4.1. A Fourier analytic characterization
- 4.2. k-intersection bodies
- 4.3. Lp-balls as k-intersection bodies
- 4.4. The second derivative test
- 4.5. Remarks and further results
Chapter 5. The Busemann-Petty Problem
- 5.1. A Fourier analytic solution
- 5.2. How can one make the answer affirmative?
- 5.3. The affirmative part via spherical harmonics
- 5.4. Zvavitch's generalization to arbitrary measures
- 5.5. Remarks and further results
Chapter 6. Intersection Bodies and Lp-Spaces
- 6.1. Lp-spaces and positive definite functions
- 6.2. Schoenberg's problems on positive definite functions
- 6.3. Intersection bodies and embeddings in Lp, p < 0
- 6.4. Remarks and further results
Chapter 7. Extremal Sections of ℓq-Balls
- 7.1. The case of the cube, K. Ball's theorem
- 7.2. The case 0 <q≤2
- 7.3. Remarks and further results
Chapter 8. Projections and the Fourier Transform
- 8.1. A formula for the volume of hyperplane projections
- 8.2. Extremal hyperplane projections of ℓq-balls
- 8.3. Projection bodies
- 8.4. The Shephard problem
- 8.5. Remarks and further results
Bibliography
Index