S-elementary wavelets and the into C(K) extension property /
Let D : Rn [] Rn be an expansive, linear map, and let
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| Format: | Thesis Book |
| Language: | English |
| Published: |
[Place of publication not identified] :
[publisher not identified] ;
1997.
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| Subjects: | |
| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=739887931&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | Let D : Rn [] Rn be an expansive, linear map, and let (k1,..., kn) be arbitrary positive numbers. Then, there exists a single function s-elementary wavelet with respect to D1 that is, a function f [] L2(Rn) such that []det(D)[]j/2f(Djx + (l1k1,...,lnkn) : j,l1,...,ln = -[] ... [] forms an orthonormal basis for L2(Rn), and [] = 1E for some measurable set E. In addition, the collection of all sets E such that 1E is the Fourier transform of a wavelet generates the Borel []-algebra, and the collection of all s- elementary wavelets is path-connected. Let X be a separable, infinite dimensional, uniformly smooth Banach space. Then there exists a Banach space Y [] X, a norm-one linear map T : X [] C(K), and an [] > 0 such that there is no extension [] :Y [] C(K) of T which satisfies [] < 1 +, []. |
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| Item Description: | Vita. "Major Subject: Mathematics". |
| Physical Description: | vi, 86 leaves ; 28 cm. Issued also on microfiche from University Microfilms Inc. |
| Bibliography: | Includes bibliographical references: pages 84-85. |