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

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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https://hal.inria.fr/inria-00429898
Contributor : Juliette Leblond Connect in order to contact the contributor
Submitted on : Friday, November 6, 2009 - 10:07:51 AM
Last modification on : Saturday, June 25, 2022 - 11:02:45 PM
Long-term archiving on: : Thursday, June 17, 2010 - 7:27:52 PM

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  • HAL Id : inria-00429898, version 1
  • ARXIV : 0911.1441

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Laurent Baratchart, Juliette Leblond, Fabien Seyfert. Constrained extremal problems in the Hardy space H2 and Carleman's formulas. [Research Report] RR-7087, INRIA. 2009, pp.50. ⟨inria-00429898⟩

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