Reproducing properties of differentiable Mercer-like kernels

DOI10.1002/mana.201100072zbMath1381.42013OpenAlexW2001424293MaRDI QIDQ2892947

Valdir A. Menegatto, José Claudinei Ferreira

Publication date: 25 June 2012

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.201100072

zbMATH Keywords

reproducing kernel Hilbert spacespositive integral operatorsinclusion mapreproducing propertyterm-by-term differentiationMercer theory

Mathematics Subject Classification ID

Integral operators (45P05) Positive definite functions in one variable harmonic analysis (42A82) Eigenvalue problems for integral equations (45C05) Positive definite functions on groups, semigroups, etc. (43A35)

Related Items (9)

Error analysis on Hérmite learning with gradient data ⋮ The kernel regularized learning algorithm for solving Laplace equation with Dirichlet boundary ⋮ An extension of Mercer's theory to \(L^p\) ⋮ Estimates on the derivatives and analyticity of positive definite functions on \(\mathbb{R}^m\) ⋮ Simultaneous confidence bands for functional data using the Gaussian kinematic formula ⋮ Reproducing Properties of Holomorphic Kernels on Balls of ℂ^q ⋮ On a collocation point of view to reproducing kernel methods ⋮ A least square point of view to reproducing kernel methods to solve functional equations ⋮ Differentiability of bizonal positive definite kernels on complex spheres

Cites Work

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• Mercer theorem for RKHS on noncompact sets
• Positive definite matrices and integral equations on unbounded domains
• Eigenvalues of integral operators defined by smooth positive definite kernels
• On the nuclearity of integral operators
• Reproducing kernel Hilbert spaces associated with analytic translation-invariant Mercer kernels
• Derivative reproducing properties for kernel methods in learning theory
• The covering number in learning theory
• Laplace-Beltrami differentiability of positive definite kernels on the sphere
• Application of integral operator for regularized least-square regression
• Inequalities for differentiable reproducing kernels and an application to positive integral operators
• Positive definite matrices and differentiable reproducing kernel inequalities
• Learning theory estimates via integral operators and their approximations
• On the mathematical foundations of learning
• Differentiable Positive Definite Kernels on Spheres
• Term-by-Term Differentiability of Mercer's Expansion

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