Jacobi theta-functions and systems of integer shifted Gaussian functions

DOI10.1007/S10958-011-0246-5zbMath1219.42023OpenAlexW2092296300MaRDI QIDQ549525

L. A. Minin, M. V. Zhuravlev, E. A. Kiselev, Sergeĭ Mikhaĭlovich Sitnik

Publication date: 18 July 2011

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-011-0246-5

zbMATH Keywords

cardinal interpolationorthonormal systemLagrange functionJacobi theta functionRiesz systemGaussian functioninteger translatesincomplete systeminteger shifted GaussianRiesz constants

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) General harmonic expansions, frames (42C15) Interpolation in approximation theory (41A05) Completeness of sets of functions in nontrigonometric harmonic analysis (42C30) Elliptic functions and integrals (33E05)

Related Items (6)

Proofs of some conjectures on monotonicity of ratios of Kummer, Gauss and generalized hypergeometric functions ⋮ Summation of Gaussian shifts as Jacobi's third theta function ⋮ On the application of Gaussian functions for discretization of optimal control problems ⋮ Properties of bounded stochastic processes employed in biophysics ⋮ On the Riesz constants for systems of integer translates ⋮ On the construction of biorthogonal systems for subspaces generated by integral shifts of a single function

Cites Work

• Heisenberg inequalities for wavelet states
• On a Hilbert space of analytic functions and an associated integral transform part I
• On approximate approximations using Gaussian kernels
• Orthogonalization Methods
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