Approximation in \(L_2\) by partial integrals of the multidimensional Fourier transform over the eigenfunctions of the Sturm-Liouville operator

DOI10.1134/S0081543818020104zbMath1408.41004OpenAlexW2804402253MaRDI QIDQ721516

Dmitry Gorbachev, R. A. Veprintsev, Valeriĭ I. Ivanov

Publication date: 19 July 2018

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543818020104

zbMATH Keywords

Fourier transformmodulus of continuitySturm-Liouville operatorJackson inequalityGauss quadrature formula\(L_2\) space

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17)

Related Items (4)

НЕКОТОРЫЕ ЭКСТРЕМАЛЬНЫЕ ЗАДАЧИ ДЛЯ ПРЕОБРАЗОВАНИЯ ФУРЬЕ ПО СОБСТВЕННЫМ ФУНКЦИЯМ ОПЕРАТОРА ШТУРМА–ЛИУВИЛЛЯ ⋮ НЕКОТОРЫЕ ЭКСТРЕМАЛЬНЫЕ ЗАДАЧИ ГАРМОНИЧЕСКОГО АНАЛИЗА И ТЕОРИИ ПРИБЛИЖЕНИЙ ⋮ Вторая экстремальная задача Логана для преобразования Фурье по собственным функциям оператора Штурма–Лиувилля ⋮ Turán, Fejér and Bohman extremal problems for the multivariate Fourier transform in terms of the eigenfunctions of a Sturm-Liouville problem

Cites Work

• Unnamed Item
• Unnamed Item
• Approximation in \(L_2\) by partial integrals of the Fourier transform over the eigenfunctions of the Sturm-Liouville operator
• Approximation of the multidimensional Jacobi transform in \(L_2\) by partial integrals
• Two related extremal problems for entire functions of several variables
• Jackson inequalities on sphere in \(L_ 2\)
• Optimal argument in the sharp Jackson inequality in the space \(L_2\) with hyperbolic weight
• Optimal arguments in Jackson's inequality in the power-weighted space \(L_2(\mathbb R^d)\)
• Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type
• Extremum problems for entire functions of exponential spherical type

This page was built for publication: Approximation in \(L_2\) by partial integrals of the multidimensional Fourier transform over the eigenfunctions of the Sturm-Liouville operator