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http://hdl.handle.net/11375/8522
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DC Field | Value | Language |
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dc.contributor.advisor | Stewart, James D. | en_US |
dc.contributor.author | Younis, Muhammad S. | en_US |
dc.date.accessioned | 2014-06-18T16:43:09Z | - |
dc.date.available | 2014-06-18T16:43:09Z | - |
dc.date.created | 2010-12-21 | en_US |
dc.date.issued | 1974-08 | en_US |
dc.identifier.other | opendissertations/3721 | en_US |
dc.identifier.other | 4738 | en_US |
dc.identifier.other | 1704944 | en_US |
dc.identifier.uri | http://hdl.handle.net/11375/8522 | - |
dc.description.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> | en_US |
dc.subject | Mathematics | en_US |
dc.subject | Mathematics | en_US |
dc.title | Fourier Transforms of Lipschitz Functions on Compact Groups | en_US |
dc.type | thesis | en_US |
dc.contributor.department | Mathematics | en_US |
dc.description.degree | Doctor of Philosophy (PhD) | en_US |
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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