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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

References

1. Boas, R. P., Entire functions (New York, 1954).Google Scholar
2. Buck, R. C., Interpolation series, Trans. Amer. Math. Soc, 64 (1948), 283–298.Google Scholar
3. Buck, R. C., On admissibility of sequences and a theorem of Polya, Comment. Math. Helv., 27 (1953), 75–80.Google Scholar
4. Churchill, W., Expansion, uniqueness, and admissibility properties of generalized difference functionals, unpublished master's thesis, Miami University, 1962.Google Scholar
5. DeMar, R. F., Existence of interpolating functions of exponential type, Trans. Amer. Math. Soc, 105 (1962), 359–373.Google Scholar
6. DeMar, R. F., A uniqueness theorem for entire functions, Proc. Amer. Math. Soc., 16 (1965), 69–71.Google Scholar
7. DeMar, R. F., On a theorem concerning existence of interpolating functions, Trans. Amer. Math. Soc., 114 (1965), 23–29.Google Scholar
8. Dienes, P., The Taylor series (New York, 1931).Google Scholar
9. Gontcharoff, W., Recherches sur les dérivées successives des fonctions analytiques. Généralisation de la série d'Abel, Ann. Sci. Ecole Norm. Sup., 47 (1930), 1–78.Google Scholar
10. Kober, K., Dictionary of conformai representations (New York, 1952).Google Scholar