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Separation of singularities of analytic functions with preservation of boundedness


Author: V. P. Khavin
Translated by: S. V. Kislyakov
Original publication: Algebra i Analiz, tom 16 (2004), nomer 1.
Journal: St. Petersburg Math. J. 16 (2005), 259-283
MSC (2000): Primary 30E99
DOI: https://doi.org/10.1090/S1061-0022-04-00850-7
Published electronically: December 17, 2004
MathSciNet review: 2068355
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Abstract | References | Similar Articles | Additional Information

Abstract: For which pairs $(O_1,O_2)$ of open sets on the complex plane is it true that the operator

\begin{displaymath}J:(f_1,f_2)\mapsto (f_1+f_2)\vert(O_1\cap O_2) \end{displaymath}

from $H^{\infty}(O_1)\times H^{\infty}(O_2)$ to $H^{\infty}(O_1\cap O_2)$ is a surjection? In the first part of the paper, a method is indicated for constructing pairs without this property. In the second part, for some classes of pairs $(O_1,O_2)$ a right inverse for $J$ is constructed explicitly. The paper continues the previous studies of the author jointly with A. H. Nersessian and J. Ortega Cedrá.


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Additional Information

V. P. Khavin
Affiliation: St. Petersburg State University, Department of Mathematics and Mechanics, Petrodvorets, Bibliotechnaya Pl. 2, St. Petersburg 198504, Russia

DOI: https://doi.org/10.1090/S1061-0022-04-00850-7
Keywords: Bounded analytic function, Cauchy potential, plane continuum, separation of singularities
Received by editor(s): September 23, 2003
Published electronically: December 17, 2004
Dedicated: Dedicated to Mikhail Shlemovich Birman on the occasion of his 75th birthday
Article copyright: © Copyright 2004 American Mathematical Society