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Frames and reproducing kernels in a Hilbert space

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Frames and reproducing kernels in a Hilbert space

Das, Suporna (2000) Frames and reproducing kernels in a Hilbert space. Masters thesis, Concordia University.

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Abstract

Let H be a Hilbert space. A set of vectors [Special characters omitted.] ✹ H, i = 1, 2,..., n , x ✹ X , where X is a locally compact space with Borel measure v on it, constitute a rank-n continuous frame, F ([Special characters omitted.] , A, n ) if for each x ✹ X the set [Special characters omitted.] is linearly independent and there exists a positive operator A ✹ GL ( H ) such that [Special characters omitted.] Further the frame becomes discrete if (*) is replaced by [Special characters omitted.] We first study discrete frames and then move to the continuous case, where we develop a connection between frames and reproducing kernels and using this connection we categorize the frames into various kinds. Finally space H using reproducing kernel Hilbert spaces H K on H = L 2 ( X, v, C n ).

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Das, Suporna
Pagination:vi, 59 leaves ; 29 cm.
Institution:Concordia University
Degree Name:Theses (M.Sc.)
Program:Dept. of Mathematics and Statistics
Date:2000
Thesis Supervisor(s):Ali, S. Twareque
ID Code:1127
Deposited By:Concordia University Libraries
Deposited On:27 Aug 2009 13:16
Last Modified:08 Dec 2010 10:18
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