This article is cited in 4 papers

Calculation of the Riesz constants and orthogonalization for incomplete systems of coherent states by means of theta functions

E. A. Kiselev, L. A. Minin, I. Ya. Novikov

Voronezh State University

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.

Keywords: Riesz systems, coherent states, theta functions, orthogonalization, biorthogonal systems.

UDC: 517.518.8+517.988.8

MSC: 42C15, 42C40

Received: 20.05.2015 and 04.04.2016

DOI: 10.4213/sm8542

 English version: Sbornik: Mathematics, 2016, 207:8, 1127–1141

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