Fourier series and approximation on hexagonal and triangular domains

DOI10.1007/s00365-008-9034-yzbMath1181.42008arXiv0802.0316OpenAlexW2012718670MaRDI QIDQ2267386

Yuan Xu

Publication date: 1 March 2010

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.0316

Mathematics Subject Classification ID

Multidimensional problems (41A63) Rate of convergence, degree of approximation (41A25) Summability in several variables (42B08)

Related Items (15)

Positivity and Fourier integrals over regular hexagon ⋮ Distributed learning via filtered hyperinterpolation on manifolds ⋮ Approximation on the Voronoi cells of the \(A_d\) lattice ⋮ Approximation on hexagonal domains by Taylor-Abel-Poisson means ⋮ Cesàro summability of Fourier orthogonal expansions on the cylinder ⋮ Approximation properties of hexagonal Fourier series in the generalized Hölder metric ⋮ Estimation of convergence rate for multi-regression learning algorithm ⋮ Discrete Fourier analysis with lattices on planar domains ⋮ Some approximation properties of hexagonal Fourier series ⋮ Recursive three-term recurrence relations for the Jacobi polynomials on a triangle ⋮ The Poisson operator for orthogonal polynomials in the multidimensional ball ⋮ Approximation of continuous functions by matrix means of hexagonal Fourier series ⋮ On approximation of hexagonal Fourier series in the generalized Hölder metric ⋮ Degree of approximation by means of hexagonal Fourier series ⋮ Approximation by means of hexagonal Fourier series in Hölder norms

Cites Work

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• Asymptotic behavior of the Dirichlet kernel of Fourier sums with respect to a polygon
• Generalized Fourier transform on an arbitrary triangular domain
• Weighted approximation of functions on the unit sphere
• Commuting self-adjoint partial differential operators and a group theoretic problem
• Fejér means for multivariate Fourier series
• Localized polynomial frames on the interval with Jacobi weights
• Discrete Fourier Analysis, Cubature, and Interpolation on a Hexagon and a Triangle
• Orthogonal Polynomials on the Hexagon

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