Carleman approximation by non-critical functions on Riemann surfaces

Učakar, Beno (author)

We present the class of semi-admissible subsets of an open Riemann surface on which Carleman approximation by non-critical holomorphic functions is possible. In particular we characterize closed sets with empty interior on which continuous functions can be approximated by non-critical holomorphic ones. We also consider a different approach, which in some cases gives uniform approximation by non-critical holomorphic functions on more general sets than semi-admissible ones.

• Language: English
• Keywords: Carleman approximation, holomorphic functions, critical points, non-critical functions, semi-admissible sets
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.02.2026
• Year: 2026
• Number of pages: 18 str.
• Numbering: Vol. 16, iss. 1, article no. 19
• PID: 20.500.12556/RUL-179019
• UDC: 517.5
• ISSN on article: 1664-2368
• DOI: 10.1007/s13324-025-01157-4
• COBISS.SI-ID: 267095811
• Publication date in RUL: 03.02.2026

Record is a part of a journal

• Title: Analysis and mathematical physics
• Shortened title: Anal. math. phys.
• Publisher: Springer
• ISSN: 1664-2368
• COBISS.SI-ID: 18662745

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: Carlemanova aproksimacija, holomorfne funkcije, kritične točke, nekritične funkcije, semi-dopustne množice

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P1-0291
• Name: Analiza in geometrija