本書是專門為冪零李群上的非交換調(diào)和分析方向的研究生和青年教師編寫的全英文學術(shù)專著，主要介紹從事一般二步冪零李群相關(guān)工作所需的基礎(chǔ)知識、概念和原理，內(nèi)容聚焦于一般二步冪零李群的幾何分析、不可約酉表示的完整分類、傅里葉分析的相關(guān)性質(zhì)、二階次橢圓算子以及熱核的刻畫等。
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 □(數(shù)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
書單推薦
