Geodesic
Calculation of the Riesz constants and~orthogonalization for incomplete systems of coherent states by means of theta functions
Sbornik. Mathematics, Tome 207 (2016) no. 8, pp. 1127-1141

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: Riesz systems, coherent states, theta functions, orthogonalization, biorthogonal systems. 
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     title = {Calculation of the {Riesz} constants and~orthogonalization for incomplete systems of coherent states by means of theta functions},
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E. A. Kiselev; L. A. Minin; I. Ya. Novikov. Calculation of the Riesz constants and~orthogonalization for incomplete systems of coherent states by means of theta functions. Sbornik. Mathematics, Tome 207 (2016) no. 8, pp. 1127-1141. http://geodesic.mathdoc.fr/item/SM_2016_207_8_a4/