Infinite-Dimensional Stochastic Transforms and Reproducing Kernel Hilbert space

2022/09/08 by Palle E. T. Jørgensen, Jorgensen, Palle E. T., Myung-Sin Song +3
Computer Science · Mathematics · Physics and Astronomy · #41A65 #42A82 #42C15 #46E22 #47A05 #47N10 #60G15 #62H25 #68T07 #81S05 #90C20 #94A08 #94A12 #94A20 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Physics (math-ph) #Primary: 47B32. Secondary: 41A15 #Probability (math.PR) #Statistical Mechanics and Entropy #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.2209.03801

openalex publication_date 2022/09/08 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

By way of concrete presentations, we construct two infinite-dimensional transforms at the crossroads of Gaussian fields and reproducing kernel Hilbert spaces (RKHS), thus leading to a new infinite-dimensional Fourier transform in a general setting of Gaussian processes. Our results serve to unify existing tools from infinite-dimensional analysis.

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