On the Riesz constants for systems of integer translates

DOI10.1134/S0001434614070244zbMath1319.42028OpenAlexW2029355411MaRDI QIDQ2342359

L. A. Minin, E. A. Kiselev, Sergeĭ Mikhaĭlovich Sitnik, Igor Ya. Novikov

Publication date: 11 May 2015

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434614070244

zbMATH Keywords

Jacobi theta functionRiesz systemGaussian functionLorentz functionRiesz constantnode functionsystem of integer translates

Mathematics Subject Classification ID

Other functions defined by series and integrals (33E20) General harmonic expansions, frames (42C15) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58)

Related Items (6)

Proofs of some conjectures on monotonicity of ratios of Kummer, Gauss and generalized hypergeometric functions ⋮ Hermitian interpolation using window systems generated by uniform translates of the Gaussian function ⋮ Calculation of the Riesz constants and orthogonalization for incomplete systems of coherent states by means of theta functions ⋮ On the correctness of finite-rank approximations by series of shifted Gaussians ⋮ Periodic wavelet frames and time-frequency localization ⋮ Limit properties of systems of integer translates and functions generating tight Gabor frames

Uses Software

• DLMF

Cites Work

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• Jacobi theta-functions and systems of integer shifted Gaussian functions
• Convexity of quotients of theta functions
• Elliptic functions and applications
• On the sampling and recovery of bandlimited functions via scattered translates of the Gaussian
• Integral representation of Schlömilch series
• Harmonic measure of radial line segments and symmetrization
• An introduction to frames and Riesz bases

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