二步分层李群上的调和分析
出版时间:
2023-08
版次:
1
ISBN:
9787312057328
定价:
68.00
装帧:
平装
开本:
16开
页数:
192页
字数:
314千字
-
本书是专门为幂零李群上的非交换调和分析方向的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，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书。
preface
1 introduction
1.1 background
1.2 main results
2 elementary analysis of stratified lie grou
2.1 preliminaries on lie grou
2.1.1 vector fields in rn
2.1.2 lie grou on hn
2.1.3 homogeneous stratified lie grou
2.2 the sub-lacians on stratified lie grou
2.3 2-step stratified lie grou
2.3.1 characterization of 2-step stratified grou
2.3.2 some examples
3 harmonic analysis on 2-step stratified lie grou
3.1 orbit method on 2-step stratified lie grou
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-lacian 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 spe hermite functions
3.5.1 mehlers formula for the rescaled harmonic oscillator
3.5.2 spe hermite functions
3.5.3 eigenvalue problems of the a-twisted sub-lacian"
3.6 laguerre functions
3.6.1 laguerre polynomials
3.6.2 laguerre formulas for spe 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-lacians
4.2.1 heat kernels of h(λ)
4.2.2 heat kernels of l
5 appendix
5.1 abstract lie grou
5.2 left-invariant vector fields and the lie algebra
5.3 nilpotent lie grou
5.4 abstract and homogeneous stratified lie grou
bibliograply
index
index of symbols
-
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，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书。
-
目录:
preface
1 introduction
1.1 background
1.2 main results
2 elementary analysis of stratified lie grou
2.1 preliminaries on lie grou
2.1.1 vector fields in rn
2.1.2 lie grou on hn
2.1.3 homogeneous stratified lie grou
2.2 the sub-lacians on stratified lie grou
2.3 2-step stratified lie grou
2.3.1 characterization of 2-step stratified grou
2.3.2 some examples
3 harmonic analysis on 2-step stratified lie grou
3.1 orbit method on 2-step stratified lie grou
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-lacian 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 spe hermite functions
3.5.1 mehlers formula for the rescaled harmonic oscillator
3.5.2 spe hermite functions
3.5.3 eigenvalue problems of the a-twisted sub-lacian"
3.6 laguerre functions
3.6.1 laguerre polynomials
3.6.2 laguerre formulas for spe 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-lacians
4.2.1 heat kernels of h(λ)
4.2.2 heat kernels of l
5 appendix
5.1 abstract lie grou
5.2 left-invariant vector fields and the lie algebra
5.3 nilpotent lie grou
5.4 abstract and homogeneous stratified lie grou
bibliograply
index
index of symbols
查看详情
占位居中
