Properties of a discretized coherent state representation and the relation to Gabor analysis

• 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.

Nyckelord

bargmann-fock space

density theorems

phase-space

interpolation

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