TY - JOUR

T1 - Density of certain polynomial modules

AU - Baranov, A. D.

AU - Carmona, J. J.

AU - Fedorovskiy, K. Yu

PY - 2016/6/1

Y1 - 2016/6/1

N2 - In this paper the problem of density in the space C(X), for a compact set X⊂C, of polynomial modules of the type p+zdq:p,q∈C[z] for integer d>1, as well as several related problems are studied. We obtain approximability criteria for Carathéodory compact sets using the concept of a d-Nevanlinna domain, which is a new special analytic characteristic of planar simply connected domains. In connection with this concept we study the problem of taking roots in the model spaces, that is, in the subspaces of the Hardy space H2 which are invariant under the backward shift operator.

AB - In this paper the problem of density in the space C(X), for a compact set X⊂C, of polynomial modules of the type p+zdq:p,q∈C[z] for integer d>1, as well as several related problems are studied. We obtain approximability criteria for Carathéodory compact sets using the concept of a d-Nevanlinna domain, which is a new special analytic characteristic of planar simply connected domains. In connection with this concept we study the problem of taking roots in the model spaces, that is, in the subspaces of the Hardy space H2 which are invariant under the backward shift operator.

KW - Carathéodory sets

KW - D-Nevanlinna domains

KW - Model spaces K

KW - Polyanalytic polynomials

KW - Rational modules

KW - Uniform approximation

UR - http://www.scopus.com/inward/record.url?scp=84924675030&partnerID=8YFLogxK

U2 - 10.1016/j.jat.2015.02.006

DO - 10.1016/j.jat.2015.02.006

M3 - Article

AN - SCOPUS:84924675030

VL - 206

SP - 1

EP - 16

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

SN - 0021-9045

ER -