The Zorn property for holomorphic functions

Quang, Thai Thuan; Vy, Duong Thanh; Hưng, Lê Thành; Bang, Pham Hien

doi:10.4064/ap170707-11-11

Cited by 3 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Evidently, a proper complex subvariety of a domain D ⊂ C n is pluripolar. The set X := ∞ j=1 X j where X j ⊂ C, j ∈ N, is non-pluripolar if and only if each X j is nonpluripolar for all j ∈ N (see [11]).…”

Section: Preliminaries and Auxiliary Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Convergence With Respect to Admissible Sequences of Weights for a Holomorphic Space of a Sequence of Hilbert-valued Rational Functions

Thuan

2023

Preprint

View full text Add to dashboard Cite

Let D⊂ CN be a domain, H be a locally convex space with the topology defined by a sequence of Hilbert semi-norms. Denote H(D,H) the space of H-valued holomorphic functions on D and R(CN,H) the space of H-valued rational functions on CN. In this paper, we set up terminology of an admissible sequence W = {wm}m≥1 of weights for H(D, F) and study sufficient conditions on W to ensure convergence of wm(||rm-f||m2) (pointwise/ in capacity/ uniformly on compact subsets) to 0 on the whole domain D except for a pluripolar subset provided the pointwise (rapid) W-convergence of {rm-f}m≥1 to 0 occurs on a Borel non-pluripolar subset X for every f ∈ H(D,H) and {rm}m≥1 ⊂ R(CN,H), in both of cases X lies in D, and X lies in the boundary ∂D of a bounded domain D. Date: January 01, 2023. 2020 Mathematics Subject Classification. 41A20, 46G20, 31C10, 31C15

show abstract

Section: Preliminaries and Auxiliary Resultsmentioning

confidence: 99%

“…The first result is for the case where the Borel non-pluripolar subset X of D lies in D. (3) In the special case where {r m } m≥1 is a sequence of polynomials the assertion (b) was proved by Quang and his colleagues for the functions between locally convex spaces (see [11]).…”

Section: The Main Resultsmentioning

confidence: 99%

Convergence With Respect to Admissible Sequences of Weights for a Holomorphic Space of a Sequence of Hilbert-valued Rational Functions

Thuan

2023

Preprint

View full text Add to dashboard Cite

show abstract

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

Quang

Lam

2020

Complex Anal. Oper. Theory

View full text Add to dashboard Cite

Fréchet-valued meromorphic extension along a pencil of complex lines

Lam

Dai

2021

Asian-European J. Math.

View full text Add to dashboard Cite

The aim of paper is to find the condition under which a Fréchet-valued function [Formula: see text] admitting meromorphic extension along some pencil of complex lines can be meromorphically extended to a neighborhood of [Formula: see text] Some auxiliary results concerning the domains of existence for Fréchet-valued meromorphic functions, Rothstein’s theorem, Levi extension theorem for meromorphic functions with values in a locally complete space, convergence of formal power series of Fréchet-valued homogeneous polynomials are also proved in this work.

show abstract

The Zorn property for holomorphic functions

Cited by 3 publications

References 0 publications

Convergence With Respect to Admissible Sequences of Weights for a Holomorphic Space of a Sequence of Hilbert-valued Rational Functions

Convergence With Respect to Admissible Sequences of Weights for a Holomorphic Space of a Sequence of Hilbert-valued Rational Functions

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

Fréchet-valued meromorphic extension along a pencil of complex lines

Contact Info

Product

Resources

About