Carathéodory completeness on the plane
cytuj
pobierz pliki
RIS BIB ENDNOTEWybierz format
RIS BIB ENDNOTECarathéodory completeness on the plane
Data publikacji: 17.12.2019
Universitatis Iagellonicae Acta Mathematica, 2019, Tom 56, s. 15 - 21
https://doi.org/10.4467/20843828AM.19.002.12110Autorzy
Carathéodory completeness on the plane
M. A. Selby [8-10] and, independently, N. Sibony [11] proved that on the complex plane c-completeness is equivalent to c-finitely compactness. Their proofs are quite similar and are based on [4]. We give more refined equivalent conditions and, along the way, simplify the proofs.
2010 Mathematics Subject Classification. 30H05, 30H50.
1. Boivin A., Gauthier P., Holomorphic and harmonic approximation on Riemann surfaces, in the book Approximation, Complex Analysis, and Potential Theory, edited by N. Arakelian, P. M. Gauthier, and G. Sabidussi, Kluwer Academic Publishers, 2001.
2. Edigarian A., Peak points for domains in C n , Ann. Polon. Math., 114.1 (2015), 1–12.
3. Gamelin T. W., Uniform algebras, Chelsea Publishing Company, 1984.
4. Gamelin T. W., Garnett J., Distinguished homomorphisms and fiber algebras, Amer. J. Math, 92 (1970), 455–474.
5. Gogus N. G., Perkins T. L., Poletsky E. A., Non-compact versions of Edwards’ theorem, Positivity, 17 (2013), 459–473.
6. Jarnicki M., Pflug P., Invariant distances and metrics in complex analysis, De Gruyter, 2nd Extended Edition, 2013.
7. Kosiński L., Zwonek W., Proper holomorphic mappings vs. peak points and Shilov boundary, Ann. Polon. Math., 107 (2013), 97–108.
8. Selby M. A., On completeness with respect to the Carath´eodory metric, Canad. Math. Bull., 17 (1974), 261–263.
9. Selby M. A., On maximal and complete regions, Colloq. Math., 32 (1974), 119–125.
10. Selby M. A., On completeness with respect to a Carath´eodory-like metric, Colloq. Math., 39 (1978), 87–94.
11. Sibony N., Prolongement de fonctions holomorphes born´ees et metrique de Carath´eodory, Invent. Math., 29 (1975), 205–230
12. Stout E.L., The theory of uniform algebras, Bogden and Quigley Publishers, 1971.
Informacje: Universitatis Iagellonicae Acta Mathematica, 2019, Tom 56, s. 15 - 21
Typ artykułu: Oryginalny artykuł naukowy
Tytuły:
Carathéodory completeness on the plane
Carathéodory completeness on the plane
Faculty of Mathematics and Computer Science, Jagiellonian University, Krakow, Poland
Publikacja: 17.12.2019
Otrzymano: 15.02.2019
Status artykułu: Otwarte
Licencja: CC BY-NC-ND
Udział procentowy autorów:
Korekty artykułu:
-Języki publikacji:
Angielski