Local approximation of operators

DOI10.1016/j.acha.2023.01.004OpenAlexW4317233647MaRDI QIDQ2689140

Hrushikesh N. Mhaskar

Publication date: 9 March 2023

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.06392

zbMATH Keywords

approximation of operatorszonal function networksapproximation on high dimensional spheres

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Multidimensional problems (41A63) Rate of convergence, degree of approximation (41A25)

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Uses Software

• DeepONet

Cites Work

• A generalized diffusion frame for parsimonious representation of functions on data defined manifolds
• Marcinkiewicz-Zygmund measures on manifolds
• Tractability of multivariate problems. Volume I: Linear information
• On a filter for exponentially localized kernels based on Jacobi polynomials
• Some new characterizations of the Chebyshev polynomials
• Function approximation with zonal function networks with activation functions analogous to the rectified linear unit functions
• Optimal nonlinear approximation
• A quadrature formula for diffusion polynomials corresponding to a generalized heat kernel
• Approximation properties of zonal function networks using scattered data on the sphere
• Exponential tractability of linear weighted tensor product problems in the worst-case setting for arbitrary linear functionals
• Tractability for Volterra problems of the second kind with convolution kernels
• Diffusion polynomial frames on metric measure spaces
• An upper bound on Jacobi polynomials
• Weighted quadrature formulas and approximation by zonal function networks on the sphere
• Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature
• Deep vs. shallow networks: An approximation theory perspective
• ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S
• Neural Networks for Functional Approximation and System Identification
• The Random Feature Model for Input-Output Maps between Banach Spaces
• On Some Extremal Functions and their Applications in the Theory of Analytic Functions of Several Complex Variables
• Approximate Quadrature Measures on Data-Defined Spaces
• Approximation Theory and Harmonic Analysis on Spheres and Balls
• Localized Summability Kernels for Jacobi Expansions
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