对称空间和Heisenberg群上的平均周期函数的谐分析

English | PDF (True) | 2009 | 667 Pages | ISBN : 1848825323 | 7.3 MB

The theory of mean periodic functions is a subject which goes back to works of Littlewood, Delsarte, John and that has undergone a vigorous development in recent years. There has been much progress in a number of problems concerning local - pects of spectral analysis and spectral synthesis on homogeneous spaces. The study oftheseproblemsturnsouttobecloselyrelatedtoavarietyofquestionsinharmonic analysis, complex analysis, partial differential equations, integral geometry, appr- imation theory, and other branches of contemporary mathematics. The present book describes recent advances in this direction of research. Symmetric spaces and the Heisenberg group are an active ?eld of investigation at 2 the moment. The simplest examples of symmetric spaces, the classical 2-sphere S 2 and the hyperbolic plane H , play familiar roles in many areas in mathematics. The n Heisenberg groupH is a principal model for nilpotent groups, and results obtained n forH may suggest results that hold more generally for this important class of Lie groups. The purpose of this book is to develop harmonic analysis of mean periodic functions on the above spaces.

平均周期函数的理论是一个起源于Littlewood、Delsarte、John等人的课题，近年来该领域经历了迅速的发展。在许多与主空间局部谱分析和谱重构相关问题的研究方面取得了很大进展。这些问题是紧密相关的，并涉及当代数学中的谐波分析、复分析、偏微分方程、积分几何学、逼近论等多个分支的问题。本书描述了这一研究方向上的最新进展。目前，对称空间以及Heisenberg群是一个活跃的领域。最简单的对称空间包括经典的2-球面S²和双曲平面H²，在数学的许多领域中扮演着熟悉的角色。而Heisenberg群Hn是幂零李群的一个主要典范，对于这个重要的Lie群类的一般性结果可以通过在Hn上的研究成果得到启发。本书的目的在于发展上述空间上平均周期函数的谐波分析。

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