On positivity of analytic matrix functions in polydisks

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...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 328; no. 1; pp. 69 - 94
Main Authors Bolotnikov, V., Rodman, L.
Format Journal Article
LanguageEnglish
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
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Summary: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 integral formula, a function as above.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(00)00331-1