Extending positive definiteness

Cichoń, Dariusz; Stochel, Jan; Szafraniec, Franciszek

doi:10.1090/S0002-9947-2010-05268-7

Extending positive definiteness
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by Dariusz Cichoń, Jan Stochel and Franciszek Hugon Szafraniec

Trans. Amer. Math. Soc. 363 (2011), 545-577

DOI: https://doi.org/10.1090/S0002-9947-2010-05268-7

Published electronically: August 31, 2010

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Abstract:

The main result of this paper gives criteria for extendibility of mappings defined on symmetric subsets of $*$-semigroups to positive definite ones. By specifying the mappings in question we obtain new solutions of relevant issues in harmonic analysis concerning truncations of some important multivariate moment problems, like complex, two-sided complex and multidimensional trigonometric moment problems. In addition, unbounded subnormality and existence of unitary power dilation of several contractions is treated as an application of our general scheme.

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