Journal of Geometric Analysis· 2026Q1
Mapping Degree and Holomorphic Extendibility on Infinitely Connected Domains
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- Q1SCImago
- 2026year
Short summary
A continuous function on the boundary of a specific type of infinitely connected domain can be extended to a holomorphic function within the domain if and only if the degree of the function plus any non-zero holomorphic function on the boundary is non-negative.
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Key points
- The study focuses on infinitely connected domains in the complex plane, constructed by removing discs from the unit disc.
- A continuous function on the boundary of such a domain is extendable to a holomorphic function within the domain.
- This extendibility is proven to be equivalent to a condition on the degree of the function plus any non-zero boundary holomorphic function.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract Let $$D \subset \mathbb {C}$$ D ⊂ C be a bounded infinitely connected domain obtained from the open unit disc by deleting a sequence of pairwise disjoint closed subdiscs with centeres on the positive real axis, accumulating only at 1. Let A(D) be the algebra of all continuous functions on $$ \overline{D}$$ D ¯ which are holomorphic on D . We prove, that a continuous function f on bD extends to a function in A ( D ) if and only if for each $$g \in A(D)$$ g ∈ A ( D ) such that $$f+g \not = 0$$ f + g ≠ 0 on bD , the degree of $$f+g$$ f + g is non-negative.
The authors' abstract, as published at the source. Journal of Geometric Analysis, 2026 · DOI ↗
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Field: Applied Mathematics
Applied MathematicsMathematics