Fourier analysis on domains in compact groups
Publication in refereed journal

香港中文大學研究人員

引用次數
替代計量分析
.

其它資訊
摘要Let Omega be a measurable subset of a compact group G of positive Haar measure. Let mu: pi bar right arrow mu(pi) be a non-negative function defined on the dual space (G) over cap and let L-2(mu) be the corresponding Hilbert space which consists of elements (xi(pi))(pi is an element of suppp mu) satisfying Sigma mu(pi) Tr(xi(pi)xi(pi)*) < infinity, where xi(pi) is a linear operator on the representation space of pi, and is equipped with the inner product: (xi(pi))), (eta(pi))) = Sigma mu(pi) Tr(xi(pi) eta(pi)*). We show that the Fourier transform gives an isometric isomorphism from L-2(Omega) onto L-2 (mu) if and only if the restrictions to Omega of all matrix coordinate functions root mu(pi) pi(ij), pi is an element of supp mu, constitute an orthonormal basis for L-2(Omega). Finally compact connected Lie groups case is studied. (C) 2006 Elsevier Inc. All rights reserved.
著者Leung CW
期刊名稱Journal of Functional Analysis
詳細描述Available online.
出版年份2006
月份9
日期15
卷號238
期次2
出版社ACADEMIC PRESS INC ELSEVIER SCIENCE
頁次636 - 648
國際標準期刊號0022-1236
電子國際標準期刊號1096-0783
語言英式英語
關鍵詞C-infinity vectors; compact groups; Fourier transform; spectral pairs
Web of Science 學科類別Mathematics; MATHEMATICS

上次更新時間 2021-26-02 於 01:19