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On the Growth of Functions of Mean Type

Published online by Cambridge University Press:  20 January 2009

W. H. J. Fuchs
W. H. J. Fuchs
Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York.
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1. V. Bernstein, N. Levinson, R. P. Boas, Jr., and others have investigated under what conditions on the sequence

for all functions f(z) regular and of suitably restricted growth in the halfplane x≥0. (For references see [1].)

In this note the restrictions on f(z) are that f(z) is regular, and not identically zero in continuous in and that for some positive B

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 9 , Issue 2 , November 1954 , pp. 53 - 70
Copyright
Copyright © Edinburgh Mathematical Society 1954

References

REFERENCES

1Boas, R. P., “The Growth of Analytic Functions”, Duke Math. Journal, 13 (1946), 471–481.Google Scholar
2Fuchs, W. H. J., “A Generalization of Carlson's Theorem”, Journal London Math. Soc., 21 (1946), 106–110.CrossRefGoogle Scholar
4Levinson, N., Gap and Density Theorems (New York, 1940).CrossRefGoogle Scholar
5Macintyre, A. J. and Fuchs, W. H. J. “Inequalities for Logarithmic Derivatives of a Polynomial”, Journal London Math. Soc., 15 (1940), 162–168.CrossRefGoogle Scholar