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Interpolation by periods in a planar domain


Author: M. B. Dubashinskiy
Translated by: the author
Original publication: Algebra i Analiz, tom 28 (2016), nomer 5.
Journal: St. Petersburg Math. J. 28 (2017), 597-669
MSC (2010): Primary 30C85; Secondary 31A15, 30E05, 30H20, 58A14, 26D15
DOI: https://doi.org/10.1090/spmj/1465
Published electronically: July 25, 2017
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \Omega \subset \mathbb{R}^2$ be a countably connected domain. With any closed differential form of degree $ 1$ in $ \Omega $ with components in $ L^2(\Omega )$ one associates the sequence of its periods around the holes in $ \Omega $, that is around the bounded connected components of $ \mathbb{R}^2\setminus \Omega $. For which $ \Omega $ the collection of such period sequences coincides with $ \ell ^2$? We give an answer in terms of metric properties of holes in $ \Omega $.


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Additional Information

M. B. Dubashinskiy
Affiliation: Chebyshev Laboratory, St. Petersburg State University, 14th Line 29b, Vasilyevsky Island, Saint Petersburg 199178, Russia
Email: mikhail.dubashinskiy@gmail.com

DOI: https://doi.org/10.1090/spmj/1465
Keywords: Infinitely-connected domain, periods of forms, interpolation, Riesz basis, harmonic functions
Received by editor(s): November 27, 2015
Published electronically: July 25, 2017
Additional Notes: Supported by the Russian Science Foundation grant 14-21-00035
Dedicated: Dedicated to the memory of Victor Petrovich Havin
Article copyright: © Copyright 2017 American Mathematical Society

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