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An indeterminate rational moment problem and Carathéodory functions

✍ Scribed by Adhemar Bultheel; Pablo González-Vera; Erik Hendriksen; Olav NjÅstad

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
177 KB
Volume
219
Category
Article
ISSN
0377-0427

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✦ Synopsis

Let { n } ∞ n=1 be a sequence of points in the open unit disk in the complex plane and let

. We put L = span{B n : n = 0, 1, 2, . . .} and we consider the following "moment" problem: Given a positive-definite Hermitian inner product •, • in L, find all positive Borel measures on [-, ) such that

We assume that this moment problem is indeterminate. Under some additional condition on the n we will describe a one-to-one correspondence between the collection of all solutions to this moment problem and the collection of all Carathéodory functions augmented by the constant ∞.

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