On Bitangential Interpolation in the Time-Varying Setting for Hilbert-Schmidt Operators: The Continuous Time Case

D. Alpay, V. Bolotnikov, B. Freydin, Y. Peretz

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The Hilbert space of lower triangular Hilbert-Schmidt operators on the real line is a natural analogue of the Hardy space of a half-plane, where the complex numbers are now replaced by matrix-valued functions. One can associate with a bounded operator its "values" at a matrix-valued function [see Ballet al.,Oper. Theory Adv. Appl.56(1992), 52-89], and this allows [see Ballet al.,Integral Equations Operator Theory20(1994), 1-43] to define and solve the analogue of the two-sided Nudelman interpolation problem for bounded operators (which form an analogue ofH(C+)). In this paper we consider the two-sided interpolation problem with a Hilbert-schmidt norm constraint (rather than the more common operator-norm constraint) on the interpolant.

Original languageEnglish
Pages (from-to)275-292
Number of pages18
JournalJournal of Mathematical Analysis and Applications
Volume228
Issue number2
DOIs
StatePublished - 15 Dec 1998

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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