Citation
Welch, Lloyd Richard (1958) The rearrangement of functions and maximization of a convolution integral. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/B59P-3R31. https://resolver.caltech.edu/CaltechETD:etd-01192006-081053
Abstract
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
For the additive group of the real numbers, the value, at the origin, of the convolution of three non-negative integrable functions is less than or equal to the corresponding value obtained from the symmetric rearrangements of those functions. That is [...].
This problem is investigated on general groups and it is shown that under a wide interpretation of the notion of symmetric rearrangement the validity of the inequality implies serious restrictions on the group.
Both new and known results in [...] are developed using methods which in modified form yield the answer to the similar problem on the sphere.
Item Type: | Thesis (Dissertation (Ph.D.)) |
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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: | 1 January 1958 |
Record Number: | CaltechETD:etd-01192006-081053 |
Persistent URL: | https://resolver.caltech.edu/CaltechETD:etd-01192006-081053 |
DOI: | 10.7907/B59P-3R31 |
Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
ID Code: | 231 |
Collection: | CaltechTHESIS |
Deposited By: | Imported from ETD-db |
Deposited On: | 24 Jan 2006 |
Last Modified: | 21 Dec 2019 04:55 |
Thesis Files
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