Interpolating by functions from model subspaces in $H^1$

Konstantin M. Dyakonov

doi:10.1007/s00020-018-2451-9

paper

Interpolating by functions from model subspaces in $H^{1}$

arXiv:1802.06433 · doi:10.1007/s00020-018-2451-9

Abstract

Given an interpolating Blaschke product $B$ with zeros ${a_{j}}$ , we seek to characterize the sequences of values ${w_{j}}$ for which the interpolation problem $f (a_{j}) = w_{j} (j = 1, 2, \dots)$ can be solved with a function $f$ from the model subspace $H^{1} \cap B H_{0}^{1}$ of the Hardy space $H^{1}$ .

7 pages; to appear in Integral Equations and Operator Theory

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A free interpolation problem for a subspace of $H^{\infty}$

Interpolating by functions from model subspaces in H1

Abstract

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Interpolating by functions from model subspaces in $H^{1}$