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On Generalized Powers of the Difference Operator

Published online by Cambridge University Press:  20 November 2018

K. R. Unni
K. R. Unni*
Affiliation:
Northwestern University
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Sumner (3) discussed for arbitrary real λ and h, where the averaging operator ∇h is defined by

(1.1)

when f(z) is an entire function of exponential type <2π/|h|. Boas (2) gave an alternative definition of ∇h which gave Sumner's results quickly and showed that his definition is equivalent to that of Sumner.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 124 - 129
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Boas, R. P. Jr., Entire functions (New York, 1954).Google Scholar
2. Boas, R. P. Jr., On generalized averaging operators. Can. J. Math., 10 (1957), 122–126.Google Scholar
3. Sumner, D. B., A generalized averaging operator, Can. J. Math., 8 (1956), 437–446.Google Scholar
4. Sumner, D. B., Generalized powers of the difference operator, Trans. Amer. Math. Soc, 87(2) (1958), 526–540.Google Scholar