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

DOI10.1134/S000143461609025XzbMath1357.41034OpenAlexW2534744793MaRDI QIDQ509164

Valeriĭ I. Ivanov, Dmitry Gorbachev

Publication date: 9 February 2017

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

Full work available at URL: https://doi.org/10.1134/s000143461609025x

zbMATH Keywords

Fourier transformJackson's inequalityGauss quadrature formulaspace \(L_{2}\)Sturm-Liouville operator on half-line

Mathematics Subject Classification ID

Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) 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 ⋮ Approximation in \(L_2\) by partial integrals of the multidimensional Fourier transform over the eigenfunctions of the Sturm-Liouville operator

Cites Work

• Approximation of the multidimensional Jacobi transform in \(L_2\) by partial integrals
• Multidimensional Jackson theorem in \(L_ 2\).
• Jacobi functions: the addition formula and the positivity of the dual convolution structure
• Two related extremal problems for entire functions of several variables
• Jackson inequalities on sphere in \(L_ 2\)
• Optimal arguments in the Jackson-Stechkin inequality in \(L_2(\mathbb R^d)\) with Dunkl weight
• 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
• Extremal Problems for Positive-Definite Bandlimited Functions. I. Eventually Positive Functions with Zero Integral
• A Quadrature Formula Involving Zeros of Bessel Functions
• A Quadrature Formula with Zeros of Bessel Functions as Nodes
• Extremum problems for entire functions of exponential spherical type
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