Das, Suporna (2000) Frames and reproducing kernels in a Hilbert space. Masters thesis, Concordia University.
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)|
|Pagination:||vi, 59 leaves ; 29 cm.|
|Degree Name:||Theses (M.Sc.)|
|Program:||Dept. of Mathematics and Statistics|
|Thesis Supervisor(s):||Ali, S. Twareque|
|Deposited By:||Concordia University Libraries|
|Deposited On:||27 Aug 2009 13:16|
|Last Modified:||06 May 2015 11:19|
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