An abstract approach to approximation in spaces of pseudocontinuable functions
(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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https://lup.lub.lu.se/record/d604a1d3-ddcb-4319-a981-b0a142b02780
- author
- Limani, Adem LU and Malman, Bartosz LU
- organization
- publishing date
- 2022
- 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 > 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. </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}}, }