Please use this identifier to cite or link to this item:
http://hdl.handle.net/11375/8522
Title: | Fourier Transforms of Lipschitz Functions on Compact Groups |
Authors: | Younis, Muhammad S. |
Advisor: | Stewart, James D. |
Department: | Mathematics |
Keywords: | Mathematics;Mathematics |
Publication Date: | Aug-1974 |
Abstract: | <p>If a function f is in LP(G), where 1 < p ≤ 2 and G is a locally compact abelian group, it is well-known that the Fourier transform f of f lies in L^q(r), where 1/p + 1/q = 1 and r is the dual group of G. This thesis is concerned with how this fact can be strengthened if it is known that f satisfies a Lipschitz condition. For certain kinds of compact groups (the circle and a-dimensional groups) we prove that if f is in Lip(α;p) then f lies in Lᵝ(r) for β > p/(p+αp-1), and a similar result holds for the n-dimensional torus. These results are generalizations and analogues of classical theorems of Bernstein and Titchmarsh about Fourier series and integrals. Furthermore we obtain more precise information for the case p = 2.</p> |
URI: | http://hdl.handle.net/11375/8522 |
Identifier: | opendissertations/3721 4738 1704944 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Size | Format | |
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fulltext.pdf | 1.8 MB | Adobe PDF | View/Open |
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