Functions that preserve families of positive semidefinite matrices
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)].
functions preserving positive definite matrices
scientific article; zbMATH DE number 769051
scientific article