Approximation of the multidimensional Jacobi transform in \(L_2\) by partial integrals

DOI10.1134/S0001434615050193zbMath1323.41016MaRDI QIDQ745625

R. A. Veprintsev

Publication date: 14 October 2015

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

zbMATH Keywords

Jacobi functionmodulus of continuityJackson inequalityparallelepipedJacobi transformBernstein's inequality\(l_p\)-ballLebesgue-measurable function

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Approximation by other special function classes (41A30)

Related Items (6)

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 Fourier transform over the eigenfunctions of the Sturm-Liouville operator ⋮ Some extremal problems for the Fourier transform on the hyperboloid ⋮ Approximation in \(L_2\) by partial integrals of the multidimensional Fourier transform over the eigenfunctions of the Sturm-Liouville operator ⋮ 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
• Unnamed Item
• Jackson's theorem in the space \(L_{2}(\mathbb R^{d})\) with power weight
• Multidimensional Jackson theorem in \(L_ 2\).
• A new proof of a Paley-Wiener type theorem for the Jacobi transform
• Jacobi functions: the addition formula and the positivity of the dual convolution structure
• Two related extremal problems for entire functions of several variables
• 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 \(L_2(\mathbb R^d)\)
• The convolution structure for Jacobi function expansions
• Extremum problems for entire functions of exponential spherical type

This page was built for publication: Approximation of the multidimensional Jacobi transform in \(L_2\) by partial integrals