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The LpSpace of a Positive Definite Matrix of Measures and Density of Matrix Polynomials inL1

โœ Scribed by Antonio J. Duran; Pedro Lopez-Rodriguez

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
395 KB
Volume
90
Category
Article
ISSN
0021-9045

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โœฆ Synopsis

In this paper we study the space L p ( +), 1 p + , + being a positive definite matrix of measures. We prove that the set of all positive definite matrices of measures having the same moments as those of + is compact in the vague topology, and we give a density result for L 1 ( +) which is an extension to the matrix case of the classical result for scalar polynomials and positive measures due to Naimark.

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## Abstract In this paper, some necessary and sufficient conditions for the existence of the positive definite solutions for the matrix equation __X__ + __A__^\*^__X__^โˆ’ฮฑ^__A__ = __Q__ with ฮฑ โˆˆ (0, โˆž) are given. Iterative methods to obtain the positive definite solutions are established and the rat