Weighted Sobolev orthogonal polynomials on the unit ball

DOI10.1016/j.jat.2013.03.004zbMath1281.42026arXiv1211.2489OpenAlexW2021572240MaRDI QIDQ390501

Teresa E. Pérez, Miguel A. Piñar, Yuan Xu

Publication date: 8 January 2014

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.2489

zbMATH Keywords

Sobolev orthogonal polynomialsgradientunit ball

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Related Items (17)

On Sobolev orthogonal polynomials on a triangle ⋮ Mixed norm estimates for the Riesz transforms on the Heisenberg group ⋮ On linearly related orthogonal polynomials in several variables ⋮ Sobolev orthogonality of polynomial solutions of second-order partial differential equations ⋮ Approximation via gradients on the ball. The Zernike case ⋮ On the Uniform Convergence of the Fourier Series by the System of Polynomials Generated by the System of Laguerre Polynomials ⋮ From Standard Orthogonal Polynomials to Sobolev Orthogonal Polynomials: The Role of Semiclassical Linear Functionals ⋮ The Riesz transform for the harmonic oscillator in spherical coordinates ⋮ On Sobolev orthogonal polynomials ⋮ RECURRENCE RELATIONS FOR SOBOLEV ORTHOGONAL POLYNOMIALS ⋮ Sobolev orthogonal polynomials of several variables on product domains ⋮ Quasi-Monte Carlo tractability of integration problem in function spaces defined over products of balls ⋮ The radial part of a class of Sobolev polynomials on the unit ball ⋮ A posteriori error estimates of spectral approximations for second order partial differential equations in spherical geometries ⋮ Recurrence Relations for Polynomials Orthonormal on Sobolev, Generated by Laguerre Polynomials ⋮ Orthogonal polynomials on the unit ball and fourth-order partial differential equations ⋮ Mixed norm estimates for the Riesz transforms associated to Dunkl harmonic oscillators

Uses Software

• OPQ

Cites Work

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• Krall-Jacobi commutative algebras of partial differential operators
• A family of Sobolev orthogonal polynomials on the unit ball
• Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports
• Sobolev orthogonal polynomials defined via gradient on the unit ball
• Determination of all coherent pairs
• Solving the nonlinear Poisson equation on the unit disk
• Orthogonal polynomials and partial differential equations on the unit ball
• Approximation Theory and Harmonic Analysis on Spheres and Balls
• Analytic aspects of Sobolev orthogonal polynomials revisited

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