Introduction to frames

Bhargava, S. (2001) Introduction to frames. pp. 97-107.

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Review : A collection of elements {ej:j∈J} in a Hilbert space H is said to be a frame for H if there exist constants A and B with 0<A≤B<∞ such that A∥h∥2H≤∑j∈J|⟨h,ej⟩|2≤B∥h∥2H,for all h∈H. The article shows a reconstruction formula for frames, that is, every frame {ej:j∈J} in H has a dual frame {e˜j:j∈J} such that ∑j∈J⟨h,ej⟩e˜j=h=∑j∈J⟨h,e˜j⟩ej,for all h∈H. The layout and the content of the paper is as in Section 3.2 of the book by I. C. Daubechies [Ten lectures on wavelets, SIAM, Philadelphia, PA, 1992; MR1162107 (93e:42045)].

Item Type: Article
Subjects: Physical Sciences > Mathematics
Divisions: Constituent Colleges > Yuvaraja's College Mysore > Mathematics
Depositing User: Kodandarama
Date Deposited: 28 May 2013 07:23
Last Modified: 28 May 2013 07:23

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