Probabilistic and average linear widths of Sobolev space with Gaussian measure

DOI10.1016/S0885-064X(02)00005-5zbMath1027.46032MaRDI QIDQ1394938

Pei Xin Ye, Gen Sun Fang

Publication date: 25 June 2003

Published in: Journal of Complexity (Search for Journal in Brave)

zbMATH Keywords

Sobolev spaceGaussian measureaverage widthprobabilistic width

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (max. 100)

Average sampling numbers of multivariate periodic function spaces with a Gaussian measure ⋮ Probabilistic linear widths of Sobolev space with Jacobi weights on \([-1,1\)] ⋮ Gel'fand widths of Sobolev classes of functions in the average setting ⋮ Linear \(n\)-widths of diagonal matrices in the average and probabilistic settings ⋮ Estimates of probabilistic widths of the diagonal operator of finite-dimensional sets with the Gaussian measure ⋮ Approximation of multivariate periodic functions on the space with a Gaussian measure ⋮ Probabilistic and average widths of Sobolev spaces on compact two-point homogeneous spaces equipped with a Gaussian measure ⋮ Probabilistic and average linear widths of weighted Sobolev spaces on the ball equipped with a Gaussian measure ⋮ Linear widths of a multivariate function space equipped with a Gaussian measure ⋮ Probabilistic and average widths of multivariate Sobolev spaces with mixed derivative equipped with the Gaussian measure

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Average \(n\)-width of point set in Hilbert space
• Gaussian measures in Banach spaces
• Linear widths of function spaces equipped with the Gaussian measure
• \(\mu\)-average \(n\)-widths on the Wiener space
• Average error bounds of best approximation of continuous functions on the Wiener space
• Average-case analysis of numerical problems
• Probabilistic and average linear width in \(L_ \infty\)-norm with respect to \(r\)-fold Wiener measure
• ON LINEAR WIDTHS OF SOBOLEV CLASSES AND CHAINS OF EXTREMAL SUBSPACES
• DIAMETERS OF SETS IN NORMED LINEAR SPACES AND THE APPROXIMATION OF FUNCTIONS BY TRIGONOMETRIC POLYNOMIALS

This page was built for publication: Probabilistic and average linear widths of Sobolev space with Gaussian measure