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Bounded index and summability methods

Published online by Cambridge University Press:  09 April 2009

G. H. Fricke  and
R. E. Powell
G. H. Fricke
Affiliation:
Wright State University, Dayton, Ohio, U.S.A.
R. E. Powell
Affiliation:
Kent State University, Kent, Ohio, U.S.A.
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An entire function f(z) is of bounded index if there exists a non-negative integer N such that . The least such integer N is called the index of f (se Lepson (1966)).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 1 , February 1976 , pp. 79 - 87
Copyright
Copyright © Australian Mathematical Society 1976

References

Fricke, G. H. (to appear), ‘A characterization of functions of bounded index’.Google Scholar
Fricke, G. H. and Powell, R. E. (1970), ‘A theorem on entire methods of summation’, Comp. Math. 22, 253–259.Google Scholar
Knopp, K. and Lorentz, G. G. (1949), ‘Beiträge zur absoluten Limitierung’, Arch. Math. 2, 10–16.CrossRefGoogle Scholar
Lepson, B. (1966), Differential equations of infinite order, hyperdirichlet series and entire functions of bounded index. (Lecture notes, Summer Institute on Entire Functions, University of California, La Jolla).Google Scholar
Powell, R. E. and Shah, S. M. (1972), Summability Theory and Applications (London, Van Nostrand Reinhold, 1972).Google Scholar
Shah, S. M. (1970), ‘Entire functions of unbounded index and having simple zeros’, Math. Z. 118, 193–196.Google Scholar