Infinite-dimensional stochastic transforms and reproducing kernel Hilbert space

DOI10.1007/s43670-023-00051-zarXiv2209.03801MaRDI QIDQ6049820

Palle E. T. Jorgensen, Myung-Sin Song, James Tian

Publication date: 18 September 2023

Published in: Sampling Theory, Signal Processing, and Data Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.03801

zbMATH Keywords

momentsgeometryinterpolationsamplingoptimizationalgorithmssplinesprincipal component analysisstochastic processesGaussian processdimension reductionFourier analysisprobabilitycovariance matrixframesinformation theoryfactorizationsmachine learningembedding problemsreproducing kernel Hilbert spacemathematical physicspositive-definite kernelsdigital image analysisKarhunen-LoèveKaczmarzsignal/image processingcomplex function-theory

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Gaussian processes (60G15) Artificial neural networks and deep learning (68T07) Quadratic programming (90C20) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) General harmonic expansions, frames (42C15) Positive definite functions in one variable harmonic analysis (42A82) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Spline approximation (41A15) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10) Sampling theory in information and communication theory (94A20) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

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