Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-25T08:17:52.171Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Bernstein, C. A. and Taylor, B. A., A new look at interpolation theory for entire functions of one variable, Advances in Math. 33 (1979), 109–143.Google Scholar
2. Leont'ev, A. F., Representation of functions by generalized Dirichlet series, Math. U.S.S.R. Izvestija 6 (1972), 1265–1277.Google Scholar
3. Taylor, B. A., Class notes for Math 704, The University of Michigan, Winter Semester (1977).Google Scholar
4. Academia Nauk S.S.R. Math. Inst. B. A. Steklov Zapiski Nauchnykh Seminarov, Isslevovaniia Po Lineinym Operatoram I Teorii Funkstii, 99 Nereshennykh Zadach Lineinoho I Kompleksnoh Analiza 81 (1978).Google Scholar