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Constrained extremal problems in the Hardy space H2 and Carleman's formulas

Authors
  • Baratchart, Laurent
  • Leblond, Juliette
  • Seyfert, Fabien
Type
Preprint
Publication Date
Nov 07, 2009
Submission Date
Nov 07, 2009
Source
arXiv
License
Yellow
External links

Abstract

We study some approximation problems on a strict subset of the circle by analytic functions of the Hardy space H2 of the unit disk (in C), whose modulus satisfy a pointwise constraint on the complentary part of the circle. Existence and uniqueness results, as well as pointwise saturation of the constraint, are established. We also derive a critical point equation which gives rise to a dual formulation of the problem. We further compute directional derivatives for this functional as a computational means to approach the issue. We then consider a finite-dimensional polynomial version of the bounded extremal problem.

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