Moment problems (Mathematics) Abelian groups Mathematics
We will study matrix-valued moment problems. First, we will study matrix-valued positive semidefinite function on a locally compact Abelian group. We will show that matrix-valued positive semidefinite functions and matrix-valued moment functions are in a one-to-one correspondence on a locally compact Abelian group. Next, we will explore the truncated matrix-valued K-moment problem on R^d, C^d, and T^d. As a consequence, we get a solution criteria for data which is indexed up to an odd-degree to admit a minimal solution. Moreover, the representing measure is easily constructed from the given data. We will use this criterion to partially solve the complex cubic moment problem and show that it is different from the results that were obtained in the quadratic case. Finally, we will extend Tchakalo's theorem, for the existence of cubature rules, to the matrix-valued case.
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Details
Title
Matrix-valued moment problems
Creators
David P. Kimsey - DU
Contributors
Hugo J. Woerdeman (Advisor) - Drexel University (1970-)
Awarding Institution
Drexel University
Degree Awarded
Doctor of Philosophy (Ph.D.)
Publisher
Drexel University; Philadelphia, Pennsylvania
Resource Type
Dissertation
Language
English
Academic Unit
College of Arts and Sciences; Drexel University; Mathematics
Other Identifier
3522; 991014632325004721
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