Polynomial hulls and an optimization problem

Details Polynomial hulls and an optimization problem Polynomial hulls and an optimization problem

2004-07-02

arxiv.org/abs/math/0407023v1

Mathematics

Complex Variables

12 pages. To appear in the Journal of Geometric Analysis. This work is the sequel to another paper by the same author, (see

Scientific paper

Let T be the unit circle in the complex plane C. This paper proves the existence of analytic structure in a compact subset K of T X C^n, where K has so-called "lineally convex" or "hypoconvex" fibers over T. It also addresses a related H-infinity optimization problem. The theorems here remove a number of unnatural assumptions required in an earlier work by the same author, "Polynomial hulls and H-infinity control for a hypoconvex constraint." (See http://www.arxiv.org/abs/math.CV/0001039)

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