Calculation of the Riesz constants and orthogonalization for incomplete systems of coherent states by means of theta functions. (August 2016)

• Record Type: Journal Article
• Authors: Kiselev, E. A.; Minin, L. A.; Novikov, I. Ya.
• Is Part Of: Sbornik. Volume 207:Number 8(2016)
• Page Start: 1127
• Page End: 1141
• Publication Date: 2016-08
• Subjects: Primary 42C15 -- 42C40; Riesz systems -- coherent states -- theta functions -- orthogonalization -- biorthogonal systems.; Mathematics -- Periodicals; 510.5
• DOI: 10.1070/SM8542
• Languages: English
• ISSNs: 1064-5616

Abstract

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.