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
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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|
|Division:||Physics, Mathematics and Astronomy|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||1 January 1958|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||24 Jan 2006|
|Last Modified:||26 Dec 2012 02:28|
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