Generalized binomial expansion on complex matrix space
type: Item
instance of: scholarly article
title: Generalized binomial expansion on complex matrix space
zbMATH Open document ID: 0914.43009
author: Hongming Ding
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-11-01T00:00:00Z
review text: Let \(V=\text{Herm}(r\mathbb{C})\) be the set of all \(r\times r\) complex Hermitian matrices and \(\Omega\subset V\) be the set of all positive-definite matrices. For an arbitrary spherical function \(\varphi_{-\mu}\) on \(\Omega\) with index \(\mu\in\mathbb{C}^r\) the author obtains the generalized binomial expansion of \(\varphi_{-\mu}(I_r-x)\) into a spherical series on the open unit ball \(D\) for the spectral norm in \(\mathbb{C}^{r\times r}\), where \(x\in\Omega\) and \(I_r\in\Omega\) is the identity matrix. As one of the corollaries the spherical transform of \(\varphi_{-\mu}(I_r+x)\) is computed.
Mathematics Subject Classification ID: 43A90
Mathematics Subject Classification ID: 41A58
zbMATH DE Number: 1217025
zbMATH Keywords: Carlson's uniqueness theorem
zbMATH Keywords: complex Hermitian matrices
zbMATH Keywords: spherical function
MaRDI profile type: Publication
full work available at URL: jmaa.1998.5911
OpenAlex ID: W1997138870
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DOI: 10.1006/JMAA.1998.5911
description: scientific article; zbMATH DE number 1217025