TY - JOUR

T1 - On Bitangential Interpolation in the Time-Varying Setting for Hilbert-Schmidt Operators

T2 - The Continuous Time Case

AU - Alpay, D.

AU - Bolotnikov, V.

AU - Freydin, B.

AU - Peretz, Y.

PY - 1998/12/15

Y1 - 1998/12/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0040685539&partnerID=8YFLogxK

U2 - 10.1006/jmaa.1998.6102

DO - 10.1006/jmaa.1998.6102

M3 - Article

AN - SCOPUS:0040685539

SN - 0022-247X

VL - 228

SP - 275

EP - 292

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -