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Properties of a discretized coherent state representation and the relation to Gabor analysis
2002 (English)In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 35, no 36, 7787-7801 p.Article in journal (Refereed) Published
Abstract [en]

Properties of a discretized coherent state representation (DCSR) and its connection to Gabor frame analysis are discussed. The DCSR approach was recently shown (Andersson L M 2001 J. Chem. Phys. 115 1158) to yield a practical computational scheme for quantum dynamics, and an iterative scheme for finding the identity operator was proposed. In the present work, we suggest a proof of fast convergence of the iterative scheme for computing the canonical dual to any given countable frame in a Hilbert space. The method of frames is concerned with the use of a non-orthogonal, over-complete set of functions for expansion of an arbitrary function. We also introduce the concept of 'representations of the identity operator' and show how to expand arbitrary vectors using the frame elements, without explicit diagonalization to an orthonormal basis. Numerical examples that illustrate the method are shown.

Place, publisher, year, edition, pages
2002. Vol. 35, no 36, 7787-7801 p.
Keyword [en]
bargmann-fock space, density theorems, phase-space, interpolation
Identifiers
URN: urn:nbn:se:kth:diva-21964ISI: 000178550500007OAI: oai:DiVA.org:kth-21964DiVA: diva2:340662
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

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