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Meromorphic Extensions of \((\cdot , W)\)-Meromorphic Functions

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Abstract

In this paper we establish some classes of subspaces W of the dual \(F'\) of a locally convex space F such that every F-valued (F, W)-meromorphic function (with/without local boundedness) on a domain D in \(\mathbb {C}^n,\) in the sense \(u \circ f\) is meromorphic for all \(u \in W,\) is meromorphic. Further, combining those results with studing on (BB)-Zorn property we give conditions for Fréchet spaces E, F and subspaces W of \(F'\) under which (F, W)-meromorphic functions can be meromorphically extended to a domain D of E from a subset \(D \cap E_B\) where \(E_B\) is the linear hull of some balanced convex compact subset B of E. Using these results we get the answers of the following questions: (1) When does the domain of meromorphy of a \((\cdot , W)\)-meromorphic function on a Riemann domain D over a Fréchet space coincide with the envelope of holomorphy of D? (2) When will \((\cdot , W)\)-meromorphic functions be able to extend meromorphically through an analytic subset of codimension \(\ge 2\) of a domain in a Fréchet space?

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Quy Nhon University, 170 An Duong Vuong, Quy Nhon, Binh Dinh, Vietnam

    Thai Thuan Quang

  2. Department of Mathematics, Pham Van Dong University, Quang Ngai, Vietnam

    Lien Vuong Lam

Authors
  1. Thai Thuan Quang
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  2. Lien Vuong Lam
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Correspondence to Thai Thuan Quang.

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Communicated by Daniel Aron Alpay.

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This article is part of the topical collection “Infinite-dimensional Analysis and Non-commutative Theory” edited by Marek Bozejko, Palle Jorgensen and Yuri Kondratiev.

The research of the authors was supported by the National Foundation for Science and Technology Development, Vietnam, 101.02-2017.304.

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Quang, T.T., Lam, L.V. Meromorphic Extensions of \((\cdot , W)\)-Meromorphic Functions. Complex Anal. Oper. Theory 14, 79 (2020). https://doi.org/10.1007/s11785-020-01038-7

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