Journal article
Generalized Gramians: Creating frame vectors in maximal subspaces
Analysis and applications, Vol.15(1), pp.123-135
01/01/2017
DOI: 10.1142/S0219530516500019
Abstract
A frame is a system of vectors S in Hilbert space H with properties which allow one to write algorithms for the two operations, analysis and synthesis, relative to S, for all vectors in H; expressed in norm-convergent series. Traditionally, frame properties are expressed in terms of an S-Gramian, G(S) (an infinite matrix with entries equal to the inner product of pairs of vectors in S); but still with strong restrictions on the given system of vectors in S, in order to guarantee frame-bounds. In this paper, we remove these restrictions on GS, and we obtain instead direct-integral analysis/synthesis formulas. Applications are given to reproducing kernel Hilbert spaces, and to random fields.
Details
- Title: Subtitle
- Generalized Gramians: Creating frame vectors in maximal subspaces
- Creators
- Palle Jorgensen - Univ Iowa, Dept Math, Iowa City, IA 52242 USAFeng Tian - Trine University
- Resource Type
- Journal article
- Publication Details
- Analysis and applications, Vol.15(1), pp.123-135
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
- DOI
- 10.1142/S0219530516500019
- ISSN
- 0219-5305
- eISSN
- 1793-6861
- Number of pages
- 13
- Language
- English
- Date published
- 01/01/2017
- Academic Unit
- Mathematics
- Record Identifier
- 9984240771102771
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