Some gap power series in multidimensional setting

Józef Siciak

Abstract


We study extensions of classical theorems on gap power series of a complex variable to the multidimensional case.


Keywords


Plurisubharmonic functions; negligible sets in \(\mathbb{C}^N\); power series; lacunary power series; multiple power series

Full Text:

PDF

References


Bieberbach, L., Analytische Fortsetzung, Springer-Verlag, Berlin, 1955.

Jarnicki, M., Jakóbczak, P., Wstep do teorii funkcji holomorficznych wielu zmiennych zespolonych, Wydawnictwo Uniwersytetu Jagiellonskiego, Kraków, 2002.

Klimek, M., Pluripotential Theory, Oxford University Press, New York, 1991.

Luh, W., Universal approximation properties of convergent power series on open sets, Analysis 6 (1986), 191-207.

Saint Raymond, J., Transformations separement analytiques, Ann. Inst. Fourier (Grenoble) 40 (1990), 79-101.

Siciak, J., Generalizations of a theorem of Fatou, Zeszyty Naukowe UJ 11 (1966), 81-84.

Siciak, J., Sets in (mathbb{C}^N) with vanishing global extremal function and polynomial approximation, Ann. Fac. Sci. Toulouse 20 (2011), no. S2, 189-209.




DOI: http://dx.doi.org/10.2478/v10062-011-0023-4
Date of publication: 2016-07-27 21:54:12
Date of submission: 2016-07-27 14:37:40


Statistics


Total abstract view - 412
Downloads (from 2020-06-17) - PDF - 328

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2011 Józef Siciak