The Delsarte extremal problem for the Jacobi transform

DOI10.1134/S0001434616110043zbMath1365.49007OpenAlexW2564946985MaRDI QIDQ520578

O. I. Smirnov, Valeriĭ I. Ivanov, Dmitry Gorbachev

Publication date: 5 April 2017

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

Full work available at URL: https://doi.org/10.1134/s0001434616110043

zbMATH Keywords

Jacobi functionJacobi transformDelsarte extremal problemhyperbolic weightquadrature Markov formula

Mathematics Subject Classification ID

Linear programming (90C05) Programming in abstract spaces (90C48) Laplace transform (44A10) Existence theories for problems in abstract spaces (49J27) Harmonic analysis in one variable (42A99)

Related Items (4)

НЕКОТОРЫЕ ЭКСТРЕМАЛЬНЫЕ ЗАДАЧИ ДЛЯ ПРЕОБРАЗОВАНИЯ ФУРЬЕ ПО СОБСТВЕННЫМ ФУНКЦИЯМ ОПЕРАТОРА ШТУРМА–ЛИУВИЛЛЯ ⋮ НЕКОТОРЫЕ ЭКСТРЕМАЛЬНЫЕ ЗАДАЧИ ГАРМОНИЧЕСКОГО АНАЛИЗА И ТЕОРИИ ПРИБЛИЖЕНИЙ ⋮ Some extremal problems for the Fourier transform on the hyperboloid ⋮ Turán, Fejér and Bohman extremal problems for the multivariate Fourier transform in terms of the eigenfunctions of a Sturm-Liouville problem

Cites Work

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• 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
• New upper bounds on sphere packings. II
• Optimal argument in the sharp Jackson inequality in the space \(L_2\) with hyperbolic weight
• The sphere packing problem in dimension 8
• The sphere packing problem in dimension \(24\)
• The convolution structure for Jacobi function expansions
• 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
• Sphere-packing in Euclidean space and extremal problems for trigonometrical polynomials
• Paley–Wiener theorems for the Dunkl transform

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