A remark on Fejér and Mittag-Leffler theorems
Choose format
RIS BIB ENDNOTEA remark on Fejér and Mittag-Leffler theorems
Publication date: 09.12.2015
Universitatis Iagellonicae Acta Mathematica, 2015, Volume 52, pp. 23-28
https://doi.org/10.4467/20843828AM.15.003.3729Authors
A remark on Fejér and Mittag-Leffler theorems
We discuss some generalizations of the classical Fejer and Mittag-Leffler theorems to the case of several complex variables with applications to the Shilov and Bergman boundaries.
1. Almer B., Sur quelques probl`emes de la th´eorie des fonctions analytiques de deux variables complexes, Ark. Math., 17 (1922), 1–70.
2. Borel E., Addition au m´emoire sur les s´eries divergentes, Ann. sci. de l’E´ .N.S., 16 (1899), 132–136.
3. Casadio-Tarabusi E., Trapani S., Envelopes of holomorphy of Hartogs and circular domains, Pacific J. Math., 149 (1991), 231–249.
4. Chirka G. M., Approximation by polynomials on star-like subsets of Cn (Russian), Mat. Zametki, 14 (1973), 55–60.
5. Downarowicz M., Analytic continuation of series of homogeneous polynomials of n complex variables, Univ. Iag. Acta Math., 17 (1975), 105–114.
6. Fuks B. A., Special chapters in the theory of analytic functions of several complex variables, Translations of Mathematical Monographs, 14, AMS, Providence, R. I., 1965.
7. Gunning R., Rossi H., Analytic Functions of Several Complex Variables, Prentice-Hall, Englewood Cliffs, N.J., 1965.
8. Jarnicki M., Pflug P., Extension of Holomorphic Functions, de Gruyter Expositions in Mathematics 34, Walter de Gruyter, 2000.
9. Jarnicki M., Pflug P., A counterexample to a theorem of Bremermann on Shilov boundaries, Proc. Amer. Math. Soc., 143 (2015), 1675–1677.
10. Knopp K., Uber Polynomentwicklungen im Mittag-Lefflerschen Stern Durch Anwendung der Eulerschen Reihentransformation, Acta Math., 47 (1926), 313–335.
11. Kosiński L- ., Zwonek W., Proper holomorphic mappings vs. peak points and Shilov boundary, Ann. Polon. Math., 107 (2013), 97–108.
12. Mittag-Leffler G., Sur la repr´esentation analytique d’une branche uniforme d’une fonction monog`ene, Note 1–5, Acta Math., 23 (1900), 43–62; 24 (1901), 183–204; 24 (1901), 205–244; 26 (1902), 353–391; 29 (1905), 101–181.
Information: Universitatis Iagellonicae Acta Mathematica, 2015, Volume 52, pp. 23-28
Article type: Original article
Institute of Mathematics Faculty of Mathematics and Computer Science Jagiellonian University
Institute of Mathematics Faculty of Mathematics and Computer Science Jagiellonian University
Published at: 09.12.2015
Article status: Open
Licence: None
Percentage share of authors:
Article corrections:
-Publication languages:
English