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Interpolation in Spaces of Entire Functions in ℂN

Published online by Cambridge University Press:  20 November 2018

Lawrence Gruman
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Let {sm} be a discrete set of points in ℂN and λm any sequence of points in ℂ. We shall be interested in finding an entire function F(z) such that F(sm)=λm. This is of course easy if no restriction is placed on F, but we shall be interested in finding an F which in addition satisfies certain growth conditions.

We shall denote the variable z=(z1,..., zN), zj=xj+iyj,

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 1 , 01 March 1976 , pp. 109 - 112
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Boas, R. P., Entire Functions, Academic Press, New York (1954).Google Scholar
2. Hormander, L., An Introduction to Complex Analysis in Several Variables, Second edition, North-Holland, Amsterdam (1973).Google Scholar
3. Lelong, P., Fonctionelles analytiques et fonctions entières (n Variables), Les Presses de L’Université de Montréal (1968).Google Scholar
4. Ronkin, L. I., On real sets of uniqueness for entire functions of several variables and on the completeness of functions e1〈λ, X〉 , Siber. Math. J. 13 (1972), 638-644 (Russian); English translation: Siber. Math. J. 13 (1972), 439–443.Google Scholar