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The space of totally bounded analytic functions

Published online by Cambridge University Press:  20 January 2009

Alan L. Horwitz  and
Lee A. Rubel
Alan L. Horwitz
Affiliation:
Pennsylvania State University, Delaware County Campus, 25 Yearsley Mill Road, Media, PA 19063
Lee A. Rubel
Affiliation:
University of IllinoisDepartment of Mathematics, 1409 West Green Street, Urbana, IL 61801
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This paper is a continuation of our project on “inverse interpolation”, begun in [6]. In brief, the task of inverse interpolation is to deduce some property of a function f from some given property of the set L of its Lagrange interpolants. In the present work, the property of L is that it be a uniformly bounded set of functions when restricted to the domain of f. In particular (see Section 3), when the domain is a disc, we deduce sharp bounds on the successive derivatives of f. As a result, f must extend to be an analytic function (of restricted growth) in the concentric disc of thrice the original radius.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 30 , Issue 2 , June 1987 , pp. 229 - 246
Copyright
Copyright © Edinburgh Mathematical Society 1987

References

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