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A Multidimensional Boundary Analogue of Hartogs’s Theorem on \(\mathbf n\)-Circular Domains for Integrable Functions

  • Bairambay Otemuratov
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 264)

Abstract

In the present paper we consider integrable functions given on the boundary of \(n\)-circular domain \(D\subset \mathbb C^n\), \(n>1\) and having one-dimensional property of holomorphic extension along the families of complex lines, passing through finite number of points of \(D.\) We prove the existence of holomorphic extension of such functions in \(D.\)

Keywords

Holomorphic extension Szego kernel Poisson kernel Complex lines 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Ch. Abdirov 1, Department of MathematicsKarakalpak State UniversityNukusUzbekistan

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