Functions that preserve families of positive semidefinite matrices
type: Item
instance of: scholarly article
title: Functions that preserve families of positive semidefinite matrices
zbMATH Open document ID: 0852.43004
DOI: 10.1016/0024-3795(93)00232-O
author: Carl H. FitzGerald
author: Charles A. Micchelli
author: Allan Pinkus
published in: Linear Algebra and its Applications
publication date: 1996-12-04T00:00:00Z
review text: The authors prove some interesting results about functions which map families of positive semidefinite (or conditionally positive semidefinite) matrices into matrices of the same type. For example, let \(f: \mathbb{R}\to \mathbb{R}\) be given; then \((f (a_{jk} ))\succeq 0\) whenever \((a_{jk})\succeq 0\) is equivalent with \(f\) being entire with nonnegative coefficients. This result (also the higher-dimensional analogue) as well as further theorems (but not all) in the paper, can also be obtained easily by applying part of chapter 5 in [\textit{Ch. Berg}, \textit{J. Christensen} and the reviewer, Harmonic analysis on semigroups, Graduate Texts in Math., 100. New York etc. (1984; Zbl 0619.43001)].
reviewed by: Paul Ressel
Mathematics Subject Classification ID: 43A35
Mathematics Subject Classification ID: 26B99
zbMATH DE Number: 769051
zbMATH Keywords: positive definite matrix
zbMATH Keywords: conditionally positive definite matrix
zbMATH Keywords: functions preserving positive definite matrices
zbMATH Keywords: harmonic analysis
zbMATH Keywords: semigroups
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 769051