作者：杨志鹏著
页数：185页
出版社：中国科学技术大学出版社
出版日期：2023
ISBN：9787312057328
电子书格式：PDF
PDF下载地址
内容简介
本书是专门为幂零李群上的非交换调和分析方向的研究生和青年教师编写的全英文学术专著，主要介绍从事一般二步幂零李群相关工作所需的基础知识、概念和原理，内容聚焦于一般二步幂零李群的几何分析、不可约酉表示的完整分类、傅里叶分析的相关性质、二阶次椭圆算子以及热核的刻画等。
本书可以作为高等院校非交换调和分析方向的英文教材，也可作为青年教师或者科技工作者的参考书。
目录
Preface
1 Introduction
1.1 Background
1.2 Main results
2 Elementary analysis of stratified Lie groups
2.1 Preliminaries on Lie groups
2.1.1 Vector fields in RN
2.1.2 Lie groups on HN
2.1.3 Homogeneous stratified Lie groups
2.2 The sub-Laplacians on stratified Lie groups
2.3 2-step stratified Lie groups
2.3.1 Characterization of 2-step stratified groups
2.3.2 Some examples
3 Harmonic analysis on 2-step stratified Lie groups
3.1 Orbit method on 2-step stratified Lie groups
3.1.1 Parametrization of coadjoint orbits
3.1.2 Polarization and unitary representation
3.2 The Fourier analysis
3.2.1 Irreducible unitary representations
3.2.2 Examples
3.2.3 The Fourier transform
3.2.4 The sub-Laplacian operator
3.3 (λ,ν)-Weyl transforms
3.3.1 (λ,ν)-Fourier-Wigner transform
3.3.2 (λ,ν)-Wigner transform
3.3.3 (λ,ν)-Weyl transform
3.3.4 The A-twisted convolution
3.4 Stone-von Neumann theorem
3.5 Hermite and special Hermite functions
3.5.1 Mehler’s formula for the rescaled harmonic oscillator
3.5.2 Special Hermite functions
3.5.3 Eigenvalue problems of the A-twisted sub-Laplacian”
3.6 Laguerre functions
3.6.1 Laguerre polynomials
3.6.2 Laguerre formulas for special Hermite functions
4 Applications
4.1 Weyl-HSrmander calculus
4.1.1 Weyl-HSrmander calculus on Rn
4.1.2 The (λ,ν)-Shubin classes □(数理化公式)
4.1.3 (λ,ν)-Shubin Sobolev spaces
4.2 Heat kernels of sub-Laplacians
4.2.1 Heat kernels of H(λ)
4.2.2 Heat kernels of L
5 Appendix
5.1 Abstract Lie groups
5.2 Left-invariant vector fields and the Lie algebra
5.3 Nilpotent Lie groups
5.4 Abstract and homogeneous stratified Lie groups
Bibliograply
Index
Index of Symbols
1 Introduction
1.1 Background
1.2 Main results
2 Elementary analysis of stratified Lie groups
2.1 Preliminaries on Lie groups
2.1.1 Vector fields in RN
2.1.2 Lie groups on HN
2.1.3 Homogeneous stratified Lie groups
2.2 The sub-Laplacians on stratified Lie groups
2.3 2-step stratified Lie groups
2.3.1 Characterization of 2-step stratified groups
2.3.2 Some examples
3 Harmonic analysis on 2-step stratified Lie groups
3.1 Orbit method on 2-step stratified Lie groups
3.1.1 Parametrization of coadjoint orbits
3.1.2 Polarization and unitary representation
3.2 The Fourier analysis
3.2.1 Irreducible unitary representations
3.2.2 Examples
3.2.3 The Fourier transform
3.2.4 The sub-Laplacian operator
3.3 (λ,ν)-Weyl transforms
3.3.1 (λ,ν)-Fourier-Wigner transform
3.3.2 (λ,ν)-Wigner transform
3.3.3 (λ,ν)-Weyl transform
3.3.4 The A-twisted convolution
3.4 Stone-von Neumann theorem
3.5 Hermite and special Hermite functions
3.5.1 Mehler’s formula for the rescaled harmonic oscillator
3.5.2 Special Hermite functions
3.5.3 Eigenvalue problems of the A-twisted sub-Laplacian”
3.6 Laguerre functions
3.6.1 Laguerre polynomials
3.6.2 Laguerre formulas for special Hermite functions
4 Applications
4.1 Weyl-HSrmander calculus
4.1.1 Weyl-HSrmander calculus on Rn
4.1.2 The (λ,ν)-Shubin classes □(数理化公式)
4.1.3 (λ,ν)-Shubin Sobolev spaces
4.2 Heat kernels of sub-Laplacians
4.2.1 Heat kernels of H(λ)
4.2.2 Heat kernels of L
5 Appendix
5.1 Abstract Lie groups
5.2 Left-invariant vector fields and the Lie algebra
5.3 Nilpotent Lie groups
5.4 Abstract and homogeneous stratified Lie groups
Bibliograply
Index
Index of Symbols