Abstract
For systems of coherent states that are multiply rarefied with respect to von Neumann's complete system, we use Jacobi theta functions to obtain exact analytic expressions for the Riesz constants, investigate their behaviour as functions of the ratio of steps in the spatial and frequency domains, construct biorthogonal systems, and realize an orthogonalization procedure that preserves the structure of the windowed Fourier transform. Bibliography: 19 titles.
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