Best approximation of functions on the ball on the weighted Sobolev space equipped with a Gaussian measure
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Publication:979034
DOI10.1016/j.jat.2009.12.004zbMath1205.41031OpenAlexW2008977056MaRDI QIDQ979034
Publication date: 25 June 2010
Published in: Journal of Approximation Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jat.2009.12.004
Best approximation, Chebyshev systems (41A50) Rate of convergence, degree of approximation (41A25) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)
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Cites Work
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- Approximation of functions on the Sobolev space with a Gaussian measure
- Widths of weighted Sobolev classes on the ball
- Approximation of linear functionals on a Banach space with a Gaussian measure
- Gaussian measures in Banach spaces
- Average error bounds of best approximation of continuous functions on the Wiener space
- Average-case analysis of numerical problems
- Relations between classical, average, and probabilistic Kolmogorov widths
- Weighted approximation of functions on the unit sphere
- Approximation of functions on the Sobolev space on the sphere in the average case setting
- On the problem of optimal reconstruction
- Localized polynomial frames on the ball
- Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball
- Summability of Fourier orthogonal series for Jacobi weight on a ball in ℝ^{𝕕}