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Uniqueness Classes for Difference Functionals

Published online by Cambridge University Press:  20 November 2018

Richard F. DeMar
Richard F. DeMar*
Affiliation:
Miami University, Oxford, Ohio and University of California, Davis
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If ﹛Ln﹜ is a sequence of linear functionals on a linear space C of functions to the complex numbers, then a subspace C1 ⊂ C is a uniqueness class for ﹛Ln﹜ if a function f in C1 is uniquely determined by the sequence ﹛Ln(f)﹜ of complex numbers; i.e., if f ∈ C1 and Ln(f) = 0, n = 0, 1, 2, … , implies f = 0. For example, the class of all functions f analytic at the origin is a uniqueness class for the sequence ﹛f(n)(0)﹜ of linear functionals. Gontcharoff (9) asked the following question: Suppose, instead of ﹛f(n)(0)﹜, we use ﹛f(n)(an)﹜.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 593 - 607
Copyright
Copyright © Canadian Mathematical Society 1966

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