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

页数：

184

最新
印次时间：

2026年3月

ISBN：

978-7-04-066135-4

物料号：

66135-00

出版时间：

2026年3月

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

目录
- 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