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Dissertation
Matrix-valued moment problems
Doctor of Philosophy (Ph.D.), Drexel University
Jun 2011
DOI:
https://doi.org/10.17918/etd-3522
Abstract
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