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A UNIQUENESS THEOREM FOR BOUNDED ANALYTIC FUNCTIONS

Published online by Cambridge University Press:  01 January 1997

YURII I. LYUBARSKII  and
KRISTIAN SEIP
YURII I. LYUBARSKII
Affiliation:
Institute for Low Temperature Physics and Engineering, 47 Lenin Prospect, 310164 Kharkov, Ukraine
KRISTIAN SEIP
Affiliation:
Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7034 Trondheim, Norway
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Abstract

Suppose that K is a linear space of functions analytic in some domain D in the complex plane. A sequence Λ = (λk) of distinct points from D is said to be a set of uniqueness for K if ƒ∈K and ƒ(λk) = 0 for all k imply ƒ≡0. Depending on the dispersion and the density of Λ on the one hand, and the growth of the functions in K on the other, one may often require only |ƒ(λk)| [les ]ak for some sequence of positive numbers ak, and still conclude that ƒ≡0 for ƒ∈K. Of particular interest are sharp conditions on the decay of ak, which reflect the interplay between growth and decay of analytic functions.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 1 , January 1997 , pp. 49 - 52
Copyright
© The London Mathematical Society 1997

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