On positivity of analytic matrix functions in polydisks

• Published in: Linear algebra and its applications Vol. 328; no. 1; pp. 69 - 94
• Main Authors: Bolotnikov, V., Rodman, L.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 01.05.2001; Elsevier Science
• Subjects: Algebra; Analytic functions of several variables; Exact sciences and technology; Korányi class; Linear and multilinear algebra, matrix theory; Mathematics; Sciences and techniques of general use; Strict positivity; Korányi class; 15A48; Analytic functions of several variables; Strict positivity; Multivalued function; Matrix function; Analytical function; Positive definite matrix

We study analytic functions of several variables in the Korányi class such that, when applied to a contractive tuple of doubly commuting matrices, a positive definite matrix results. A criterion is given for a finite set to have the property that every measure supported on the set yields, via an int...