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Sbornik: Mathematics, 2016, Volume 207, Issue 1, Pages 140–154
DOI: https://doi.org/10.1070/SM8455
(Mi sm8455)
 

This article is cited in 3 scientific papers (total in 3 papers)

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

K. Yu. Fedorovskiyab

a Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow
b Bauman Moscow State Technical University
References:
Abstract: We consider the question of the density in the space $L^p$, $1\leq p\leq\infty$, on the unit circle, of the subspaces $H^p+\sum_{k=1}^mw_kH^p$, where $H^p$ is the standard Hardy space and $w_1,\dots,w_m$ are given functions in the class $L^\infty$. This question is closely related to problems of uniform and $L^p$-approximations of functions by polyanalytic polynomials on the boundaries of simple connected domains in $\mathbb C$. 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 $\mathbb C$, which are related to the pseudocontinuation property of bounded holomorphic functions.
Bibliography: 19 titles.
Keywords: Nevanlinna domain, $d$-Nevanlinna domain, pseudocontinuation, polyanalytic polynomial, uniform approximation, $L^p$-approximation.
Funding agency Grant number
Russian Science Foundation 14-21-00025
This research was supported by the Russian Science Foundation (project no. 14-21-00025).
Received: 02.12.2014 and 12.07.2015
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: Primary 30E10, 30G20; Secondary 41A10
Language: English
Original paper language: Russian
Citation: K. Yu. Fedorovskiy, “On the density of certain modules of polyanalytic type in spaces of integrable functions on the boundaries of simply connected domains”, Sb. Math., 207:1 (2016), 140–154
Citation in format AMSBIB
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\paper 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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\issue 1
\pages 140--154
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  • https://doi.org/10.1070/SM8455
  • https://www.mathnet.ru/eng/sm/v207/i1/p151
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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