Skip to Main content Skip to Navigation
Reports

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.
Document type :
Reports
Complete list of metadata

Cited literature [37 references]  Display  Hide  Download

https://hal.inria.fr/inria-00429898
Contributor : Juliette Leblond <>
Submitted on : Friday, November 6, 2009 - 10:07:51 AM
Last modification on : Thursday, February 7, 2019 - 3:46:37 PM
Long-term archiving on: : Thursday, June 17, 2010 - 7:27:52 PM

Files

RR-7087.pdf
Files produced by the author(s)

Identifiers

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

Collections

Citation

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⟩

Share

Metrics

Record views

355

Files downloads

384