This article is cited in 3 papers

On Meromorphic Continuation in a Fixed Direction

A. A. Atamuratov

Al-Kharezmi Urgench State University, Khorezm, Uzbekistan

Abstract: In the present paper, we prove a local boundary version of the well-known Rothstein lemma about the meromorphic continuation with respect to one of the complex variables. The statement is simple, and the proof is based on the well-known Hadamard formulas for the radii of meromorphy, on recent results of Imomkulov about the boundary properties of sequences of plurisubharmonic functions, and on the Rothstein lemma.

Keywords: meromorphic function, meromorphic continuation, analytic function, subharmonic function, plurisubharmonic function, radius of meromorphy, Hadamard determinant.

UDC: 517.55

Received: 07.12.2007
Revised: 19.01.2009

DOI: 10.4213/mzm8497

 English version: Mathematical Notes, 2009, 86:3, 301–305

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