Constructive Approximation

, Volume 14, Issue 1, pp 41–56

Hardy Approximation to Lp Functions on Subsets of the Circle with 1< =p< = infinity

  • L. Baratchart
  • J. Leblond
Article

DOI: 10.1007/s003659900062

Cite this article as:
Baratchart, L. & Leblond, J. Constr. Approx. (1998) 14: 41. doi:10.1007/s003659900062

Abstract.

We consider approximation of Lp functions by Hardy functions on subsets of the circle for \(1 \leq p < \infty\) . After some preliminaries on the possibility of such an approximation which are connected to recovery problems of the Carleman type, we prove existence and uniqueness of the solution to a generalized extremal problem involving norm constraints on the complementary subset.

Key words. Lp Analytic approximationRecovery of Hp functions Extremal problems in Hardy spaces. AMS Classification. 30D55, 30E10, 93B30, 93C80. <lsiheader> <onlinepub>8 May, 1998 <editor>Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;R.A. DeVore E.B. Saff&lsilt;/a&lsigt; <pdfname>14n1p41.pdf <pdfexist>yes <htmlexist>no <htmlfexist>no <texexist>yes <sectionname> </lsiheader>

Copyright information

© Springer-Verlag New York 1997

Authors and Affiliations

  • L. Baratchart
    • 1
  • J. Leblond
    • 2
  1. 1.INRIA, BP 93 06902 Sophia-Antipolis Cedex France FR
  2. 2.INRIA, BP 93 06902 Sophia-Antipolis Cedex France FR