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The rearrangement of functions and maximization of a convolution integral

Welch, Lloyd Richard (1958) The rearrangement of functions and maximization of a convolution integral. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-01192006-081053

Abstract

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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.))
Degree Grantor:California Institute of Technology
Major Option:Mathematics
Thesis Committee:
  • Bohnenblust, Frederic (chair)
Defense Date:1 January 1958
Record Number:etd-01192006-081053
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-01192006-081053
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:231
Collection:CaltechTHESES
Deposited By: Imported from ETD-db
Deposited On:24 Jan 2006
Last Modified:25 Dec 2012 14:58

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