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Winter 1998 Entire Functions of Order One and Infinite Type
Badih Ghusayni
Missouri J. Math. Sci. 10(1): 20-27 (Winter 1998). DOI: 10.35834/1998/1001020

Abstract

In this paper we first prove an auxiliary result that an entire function of order one and infinite type must have infinitely many non-zero zeros. We then give an explicit canonical representation for those functions. We apply the representation to prove a result and its converse about entire functions of order one and infinite type. Next, we mention a few interesting examples of entire functions of order one and infinite type. Finally, we formulate and disprove a conjecture which serves as an analogue to the Paley-Wiener Theorem for entire functions of order one and infinite type.

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Badih Ghusayni. "Entire Functions of Order One and Infinite Type." Missouri J. Math. Sci. 10 (1) 20 - 27, Winter 1998. https://doi.org/10.35834/1998/1001020

Information

Published: Winter 1998
First available in Project Euclid: 23 November 2019

zbMATH: 1097.30517
MathSciNet: MR1611324
Digital Object Identifier: 10.35834/1998/1001020

Rights: Copyright © 1998 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.10 • No. 1 • Winter 1998
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