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Necessary Conditions for UniversalInterpolation in

Published online by Cambridge University Press:  20 November 2018

W. A. Squires
W. A. Squires*
Affiliation:
California Institute of Technology, Pasadena, California
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Let be the space of Fourier transforms of distributions with compact support, or equivalently, the space of entire functions h satisfying the growth condition

(1)

where p(z) = |Imz| + log (1 + |z|2) and A, B are constants depending only on h. A sequence with |zk| ↑ ∞ is said to be a universal interpolation sequence for if for all such that

(2)

for constants A, B independent of k, there exists such that f(zk) = ak. In this note we will consider necessary conditions for universal interpolation in and more general subspaces of the entire functions.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 6 , 01 December 1981 , pp. 1356 - 1364
Copyright
Copyright © Canadian Mathematical Society 1981

References

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