Geodesic
Uniqueness Classes for Difference Functionals
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 593-607

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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 ∈ C 1 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)}. 
DeMar, Richard F. Uniqueness Classes for Difference Functionals. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 593-607. doi: 10.4153/CJM-1966-058-8
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