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On Certain Integral Functions of Order 1 and Mean Type

Published online by Cambridge University Press:  24 October 2008

M. L. Cartwright
M. L. Cartwright
Affiliation:
Girton College
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Extract

1. The object of this note is to show the relation between certain results obtained by Wiener and Paley*, and by L'evinson from the theory of Fourier transforms, and a theorem which I proved in a recent paper. We require a general theorem on the function of Phragmèn and Lindelöf:

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 31 , Issue 3 , July 1935 , pp. 347 - 350
Copyright
Copyright © Cambridge Philosophical Society 1935

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References

* Wiener, N. and Paley, R. E. A. C., “Fourier transforms in the complex domain”, American Math. Soc. Colloquium Publications, 19 (1934), 69.Google Scholar

† Levinson, N., Proc. Cambridge Phil. Soc. 31 (1935), 335–346.CrossRefGoogle Scholar

‡ Bernstein, V., Annali della R. Sc. Normale Sup. di Pisa (Sc. Fis. e Mat.) (2), 2 (1933), 381–400 (396).Google Scholar

* Cartwright, M. L., Proc. London Math. Soc. (2), 38 (1935), 179.Google Scholar

† Phragmèn, E. and Lindelöf, E., Acta Math. 31 (1908), 397–8.Google Scholar

‡ Loc. cit. p. 399.

§ Loc. cit. p. 403.

∥ Loc. cit. p. 400.

* See Cartwright, M. L., Proc. London Math. Soc. (2), 38 (1935), 440Google Scholar, Theorems X and XI. See also Lemma 7, and 534, Lemma 9 and 537, Theorem V.

† Valiron, G., Compositio Mathematica, 1 (1935), 195.Google Scholar

‡ Loc. cit. p. 168.