Title page for ETD etd-10202005-102835


Type of Document Dissertation
Author Li, Xiaoguang
URN etd-10202005-102835
Title Moment sequences and their applications
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
No Advisors Found
Keywords
  • Moment problems - Mathematics
  • Functionals
Date of Defense 1994-07-05
Availability restricted
Abstract

In this dissertation, we first present a unified treatment of compact moment problems, both the truncated and full moment cases. Second, we define the lower and upper functions Vยฑ(๐“โ‚,... ๐“n) on the convex hull of the curve In = {(t,.ยท.,tn): t ๐œ– [0,1] } for each positive integer n. Explicit formulas of these functions are derived and applied to the study of the subnormal completion problem in operator theory. Last, we show that certain power functions are the building blocks of completely positive functions; by our definition, these functions are the continuous functions on the interval [0, 1] that map each Hausdorff moment sequence of a probability measure into another one.

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