Geometric condition for universal interpolation in

Author:
William A. Squires

Journal:
Trans. Amer. Math. Soc. **280** (1983), 401-413

MSC:
Primary 30E05; Secondary 30D15, 42A38

DOI:
https://doi.org/10.1090/S0002-9947-1983-0712268-7

MathSciNet review:
712268

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Abstract: It is known that if is an entire function of exponential type and with for constants , independent of , then is a universal interpolation sequence. That is, given any sequence of complex numbers such that for constants independent of then there exists of exponential type such that . This note is concerned with finding geometric conditions which make a universal interpolation sequence for various spaces of entire functions. For the space of entire functions of exponential type a necessary and sufficient condition for to be a universal interpolation sequence is that , where is the number of points of in the disc of radius about , excluding , and are constants independent of . Results for the space are given but the theory is not as complete as for the above example.

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DOI:
https://doi.org/10.1090/S0002-9947-1983-0712268-7

Article copyright:
© Copyright 1983
American Mathematical Society