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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An abstract approach to approximation in spaces of pseudocontinuable functions
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by Adem Limani and Bartosz Malman PDF
Proc. Amer. Math. Soc. 150 (2022), 2509-2519 Request permission

Abstract:

We provide an abstract approach to approximation with a wide range of regularity classes $X$ in spaces of pseudocontinuable functions $K^p_\vartheta$, where $\vartheta$ 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 $K^{q}_\vartheta$ for some $q>0$, then $X$ is in fact dense in $K^p_{\vartheta }$ 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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Additional Information
  • Adem Limani
  • Affiliation: Centre for Mathematical Sciences, Lund University, SE-22 100, Lund, Sweden
  • ORCID: 0000-0002-5938-3670
  • Email: adem.limani@math.lu.se; ademlimani@gmail.com
  • Bartosz Malman
  • Affiliation: Royal Institute of Technology, KTH, SE-100 44, Stockholm, Sweden
  • MR Author ID: 1231604
  • Email: malman@kth.se
  • Received by editor(s): August 25, 2021
  • Received by editor(s) in revised form: September 19, 2021, and September 21, 2021
  • Published electronically: March 16, 2022
  • Additional Notes: The first author is the corresponding author
  • Communicated by: Javad Mashreghi
  • © Copyright 2022 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 150 (2022), 2509-2519
  • MSC (2020): Primary 46E22; Secondary 30J05
  • DOI: https://doi.org/10.1090/proc/15864
  • MathSciNet review: 4399267