Jacobi theta-functions and systems of integral shifts of Gaussian functions

Zhuravlev, M. V.; Киселев, Евгений Александрович; Minin, L. A.; Sitnik, Sergei M.

doi:10.1007/s10958-011-0246-5

Cited by 15 publications

(16 citation statements)

References 9 publications

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“…It was proved in [10] that integer shifts of the Gauss function form the Riesz system with explicit constants A G (σ) = σ √ πϑ 3 π 2 , q , B G (σ) = σ √ πϑ 3 (0, q) , q = exp − 1 4σ 2 , and ϑ 3 (t, q) -the third Jacobi theta-function [11] ϑ 3 (t, q) = ∞ k=−∞ q k 2 e 2ikt , |q| < 1.…”

Section: Riesz Constants For Shifts Of Nod Functionmentioning

confidence: 94%

“…В статье [10] показано, что целочисленные сдвиги функции Гаусса образуют систему Рисса с константами…”

Section: исходная функцияunclassified

“…Один из вариантов вычислений для данного класса задач разрабо-тан в [10], [20]. Он основан на применении дискретного преобразования Фурье и формул преобразования Пуассона для тета-функций.…”

Section: обсуждение результатовunclassified

See 2 more Smart Citations

О Константах Рисса Для Некоторых Систем Целочисленных Сдвигов

Киселев¹,

Minin²,

Новиков³

et al. 2014

Matematicheskie Zametki

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Section: Riesz Constants For Shifts Of Nod Functionmentioning

confidence: 94%

“…В статье [10] показано, что целочисленные сдвиги функции Гаусса образуют систему Рисса с константами…”

Section: исходная функцияunclassified

Section: обсуждение результатовunclassified

See 1 more Smart Citation

О Константах Рисса Для Некоторых Систем Целочисленных Сдвигов

Киселев¹,

Minin²,

Новиков³

et al. 2014

Matematicheskie Zametki

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“…We shortly consider steps to derive an infinite linear system for finding coefficients of the basic node function (4), cf. [2]- [3].…”

Section: Reducing To An Infinite System Of Linear Equationsmentioning

confidence: 99%

On the Correctness of Finite-Rank Approximations by Series of Shifted Gaussians

Sitnik

Timashov

Ushakov

2020

Lobachevskii J Math

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In this paper we consider interpolation problem connected with series by integer shifts of Gaussians. Known approaches for these problems met numerical difficulties. Due to it another method is considered based on finite-rank approximations by linear systems. The main result for this approach is to establish correctness of the finiterank linear system under consideration. And the main result of the paper is to prove correctness of the finite-rank linear system approximation. For that an explicit formula for the main determinant of the linear system is derived to demonstrate that it is non-zero.

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“…It was proved in [10] that integer shifts of the Gauss function form the Riesz system with explicit constants…”

Section: Given Functionmentioning

confidence: 99%