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An abstract approach to approximation in spaces of pseudocontinuable functions

Limani, Adem LU and Malman, Bartosz LU (2022) In Proceedings of the American Mathematical Society 150(6). p.2509-2519
Abstract

We provide an abstract approach to approximation with a wide range of regularity classes X in spaces of pseudocontinuable functions Kp Θ, where Θ is an inner function and p > 0. More precisely, we demonstrate a general principle, attributed to A. Aleksandrov, which asserts that if a certain linear manifold X is dense in Kq Θ for some q > 0, then X is in fact dense in Kp Θ for all p > 0. Moreover, for a rich class of Banach spaces of analytic functions X, we describe the precise mechanism that determines when X is dense in a certain space of pseudocontinuable functions. As a consequence, we obtain an extension of Aleksandrov's density theorem to the class of analytic functions with uniformly convergent Taylor series.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Proceedings of the American Mathematical Society
volume
150
issue
6
pages
2509 - 2519
publisher
American Mathematical Society (AMS)
external identifiers
  • scopus:85127921128
ISSN
0002-9939
DOI
10.1090/proc/15864
language
English
LU publication?
yes
id
d604a1d3-ddcb-4319-a981-b0a142b02780
date added to LUP
2022-06-10 11:02:54
date last changed
2022-06-10 11:02:54
@article{d604a1d3-ddcb-4319-a981-b0a142b02780,
  abstract     = {{<p>We provide an abstract approach to approximation with a wide range of regularity classes X in spaces of pseudocontinuable functions Kp Θ, where Θ is an inner function and p &gt; 0. More precisely, we demonstrate a general principle, attributed to A. Aleksandrov, which asserts that if a certain linear manifold X is dense in Kq Θ for some q &gt; 0, then X is in fact dense in Kp Θ for all p &gt; 0. Moreover, for a rich class of Banach spaces of analytic functions X, we describe the precise mechanism that determines when X is dense in a certain space of pseudocontinuable functions. As a consequence, we obtain an extension of Aleksandrov's density theorem to the class of analytic functions with uniformly convergent Taylor series. </p>}},
  author       = {{Limani, Adem and Malman, Bartosz}},
  issn         = {{0002-9939}},
  language     = {{eng}},
  number       = {{6}},
  pages        = {{2509--2519}},
  publisher    = {{American Mathematical Society (AMS)}},
  series       = {{Proceedings of the American Mathematical Society}},
  title        = {{An abstract approach to approximation in spaces of pseudocontinuable functions}},
  url          = {{http://dx.doi.org/10.1090/proc/15864}},
  doi          = {{10.1090/proc/15864}},
  volume       = {{150}},
  year         = {{2022}},
}