We give a characterization of onto interpolating sequences with finite associated measure for the Dirichlet space in terms of condenser capacity. In the Sobolev space H1(D) we define a natural notion of onto interpolation and we prove that the same condenser capacity condition characterizes all onto interpolating sequences. As a result, for sequences with finite associated measure, the problem of interpolation by an analytic function reduces to a problem of interpolation by a function in H1(D).

Chalmoukis, N. (2021). Onto interpolation for the Dirichlet space and for H1(D). ADVANCES IN MATHEMATICS, 381 [10.1016/j.aim.2021.107634].

Onto interpolation for the Dirichlet space and for H1(D)

Chalmoukis, N
2021

Abstract

We give a characterization of onto interpolating sequences with finite associated measure for the Dirichlet space in terms of condenser capacity. In the Sobolev space H1(D) we define a natural notion of onto interpolation and we prove that the same condenser capacity condition characterizes all onto interpolating sequences. As a result, for sequences with finite associated measure, the problem of interpolation by an analytic function reduces to a problem of interpolation by a function in H1(D).
Articolo in rivista - Articolo scientifico
Dirichlet space; Interpolation; Logarithmic capacity; Plane condensers; Reproducing kernel Hilbert spaces;
English
2021
381
107634
none
Chalmoukis, N. (2021). Onto interpolation for the Dirichlet space and for H1(D). ADVANCES IN MATHEMATICS, 381 [10.1016/j.aim.2021.107634].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/401720
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