Separation of singularities of analytic functions with preservation of boundedness

Khavin, V.

doi:10.1090/S1061-0022-04-00850-7

Separation of singularities of analytic functions with preservation of boundedness
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by V. P. Khavin
Translated by: S. V. Kislyakov

St. Petersburg Math. J. 16 (2005), 259-283

DOI: https://doi.org/10.1090/S1061-0022-04-00850-7

Published electronically: December 17, 2004

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Abstract:

For which pairs $(O_1,O_2)$ of open sets on the complex plane is it true that the operator \begin{equation*}J:(f_1,f_2)\mapsto (f_1+f_2)|(O_1\cap O_2) \end{equation*} 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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