On the density of certain modules of polyanalytic type in spaces of integrable functions on the boundaries of simply connected domains

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On the density of certain modules of polyanalytic type in spaces of integrable functions on the boundaries of simply connected domains. / Fedorovskiy, K. Y.

In: Sbornik Mathematics, Vol. 207, No. 1, 2016, p. 140-154.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{e8d9988f493f47b5a977e5e3cbb6fdcc,

title = "On the density of certain modules of polyanalytic type in spaces of integrable functions on the boundaries of simply connected domains",

abstract = "We consider the question of the density in the space Lp, 1 ≤ p ≤ ∞, on the unit circle, of the subspaces Hp+σmk=1 wkHp, where Hp is the standard Hardy space and w1,...,wm are given functions in the class L∞. This question is closely related to problems of uniform and Lp-approximations of functions by polyanalytic polynomials on the boundaries of simple connected domains in ℂ. The obtained results are formulated in terms of Nevanlinna and d-Nevanlinna domains, that is, in terms of special analytic characteristics of simply connected domains in ℂ, which are related to the pseudocontinuation property of bounded holomorphic functions",

keywords = "D-Nevanlinna domain, L-approximation, Nevanlinna domain, Polyanalytic polynomial, Pseudocontinuation, Uniform approximation",

author = "Fedorovskiy, {K. Y.}",

note = "Publisher Copyright: {\textcopyright} 2016 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.",

year = "2016",

doi = "10.1070/SM8455",

language = "English",

volume = "207",

pages = "140--154",

journal = "Sbornik Mathematics",

issn = "1064-5616",

publisher = "Turpion Ltd.",

number = "1",

}

RIS

TY - JOUR

T1 - On the density of certain modules of polyanalytic type in spaces of integrable functions on the boundaries of simply connected domains

AU - Fedorovskiy, K. Y.

PY - 2016

Y1 - 2016

N2 - We consider the question of the density in the space Lp, 1 ≤ p ≤ ∞, on the unit circle, of the subspaces Hp+σmk=1 wkHp, where Hp is the standard Hardy space and w1,...,wm are given functions in the class L∞. This question is closely related to problems of uniform and Lp-approximations of functions by polyanalytic polynomials on the boundaries of simple connected domains in ℂ. The obtained results are formulated in terms of Nevanlinna and d-Nevanlinna domains, that is, in terms of special analytic characteristics of simply connected domains in ℂ, which are related to the pseudocontinuation property of bounded holomorphic functions

AB - We consider the question of the density in the space Lp, 1 ≤ p ≤ ∞, on the unit circle, of the subspaces Hp+σmk=1 wkHp, where Hp is the standard Hardy space and w1,...,wm are given functions in the class L∞. This question is closely related to problems of uniform and Lp-approximations of functions by polyanalytic polynomials on the boundaries of simple connected domains in ℂ. The obtained results are formulated in terms of Nevanlinna and d-Nevanlinna domains, that is, in terms of special analytic characteristics of simply connected domains in ℂ, which are related to the pseudocontinuation property of bounded holomorphic functions

KW - D-Nevanlinna domain

KW - L-approximation

KW - Nevanlinna domain

KW - Polyanalytic polynomial

KW - Pseudocontinuation

KW - Uniform approximation

UR - http://www.scopus.com/inward/record.url?scp=84963543046&partnerID=8YFLogxK

U2 - 10.1070/SM8455

DO - 10.1070/SM8455

M3 - Article

AN - SCOPUS:84963543046

VL - 207

SP - 140

EP - 154

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 1

ER -

ID: 86669439