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.)) |
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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): |
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Thesis Committee: |
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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: | 02 Aug 2024 22:57 |
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