A Counterexample in the Theory of Fourier Transforms in the Complex Domain

Citation

Delaney, William Kenneth (1975) A Counterexample in the Theory of Fourier Transforms in the Complex Domain. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/8s0b-ck03. https://resolver.caltech.edu/CaltechTHESIS:08312021-161900257

Abstract

The Borel transform of an entire function of exponential type is defined outside a closed bounded convex set D. Paley and Wiener have given a necessary and sufficient condition on the entire function F(z) such that φ(w), the Borel transform of F(z), is contained in E²(ℂ\D) for the case when D is a line segment. Kacnel'son has shown that the natural extension of this result provides a necessary condition for a general closed bounded convex set D. Here, by counterexample, we show that the natural extension does not provide a sufficient condition.

Item Type:	Thesis (Dissertation (Ph.D.))
Subject Keywords:	Mathematics
Degree Grantor:	California Institute of Technology
Division:	Physics, Mathematics and Astronomy
Major Option:	Mathematics
Thesis Availability:	Public (worldwide access)
Research Advisor(s):	Luxemburg, W. A. J. (advisor) Bohnenblust, Henri Frederic (co-advisor)
Thesis Committee:	Luxemburg, W. A. J. (chair) Bohnenblust, Henri Frederic (co-chair)
Defense Date:	23 May 1975
Record Number:	CaltechTHESIS:08312021-161900257
Persistent URL:	https://resolver.caltech.edu/CaltechTHESIS:08312021-161900257
DOI:	10.7907/8s0b-ck03
Default Usage Policy:	No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:	14348
Collection:	CaltechTHESIS
Deposited By:	Benjamin Perez
Deposited On:	31 Aug 2021 17:17
Last Modified:	31 Aug 2021 17:18

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