Infinite-dimensional stochastic transforms and reproducing kernel Hilbert space

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 ex...

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Bibliographic Details
Published in:Sampling theory, signal processing, and data analysis signal processing, and data analysis, 2023-06, Vol.21 (1), Article 12
Main Authors: Jorgensen, Palle E. T., Song, Myung-Sin, Tian, James
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
approximation
Data science
harmonic analysis
Machine Learning
Mathematics
Mathematics and Statistics
Original Article
Signal,Image and Speech Processing
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Summary: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.
ISSN:2730-5716
2730-5724
DOI:10.1007/s43670-023-00051-z