Abstract
LetD be a domain in ℝn (n≥1) andx 0 ∈D. We prove that a necessary and sufficient condition for the existence of a semicontinuous regular methodA such that the series expansion of any real-analytic functionf inD in homogeneous polynomials aroundx 0 is uniformly summed by this method tof(x) on compact subsets ofD is thatD be rectilinearly star-shaped with respect tox 0.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. Cooke,Infinite Matrices and Sequence Spaces, London (1950).
B. V. Shabat,Introduction to Complex Analysis [in Russian], Vol. 2, Nauka, Moscow, (1985).
A. I. Markushevich, “Analytic continuation and superconvergence,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],45, No. 6, 239–241 (1944).
A. I. Markushevich,The Theory of Analytic Functions [in Russian], Vol. 2, Nauka, Moscow (1968).
Author information
Authors and Affiliations
Additional information
Translated fromMatematicheskie Zametki, Vol. 60, No. 5, pp. 708–714, November, 1996.
In conclusion, I wish to my sincere gratitude to my scientific supervisor Prof. Dolzhenko for setting the problem and his attention to my work.
This research was supported by the Russian Foundation for Basic Research under grant No. 93-01-00236 and by the International Science Foundation under grant No. NCF000.
Rights and permissions
About this article
Cite this article
Pokrovskii, A.V. Analytic continuation and superconvergence of series of homogeneous polynomials. Math Notes 60, 531–535 (1996). https://doi.org/10.1007/BF02309167
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02309167