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Separation of singularities of analytic functions with preservation of boundedness

Author(s): V. P. Khavin
Translated by: S. V. Kislyakov
Original publication: Algebra i Analiz, tom 16 (2004), vypusk 1.
Journal: St. Petersburg Math. J. 16 (2005), 259-283.
MSC (2000): Primary 30E99
Posted: December 17, 2004
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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: 10.1090/S1061-0022-04-00850-7
PII: S 1061-0022(04)00850-7
Keywords: Bounded analytic function, Cauchy potential, plane continuum, separation of singularities
Received by editor(s): 23/SEP/2003
Posted: December 17, 2004
Dedicated: Dedicated to Mikhail Shlemovich Birman on the occasion of his 75th birthday
Copyright of article: Copyright 2004, American Mathematical Society

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