Sampling Theory, Signal Processing, and Data Analysis
Mathematics & Statistics
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.
Song, Myung-Sin; Jorgensen, Palle; and Tian, James Feng, "Infinite-dimensional stochastic transforms and reproducing kernel Hilbert space" (2023). SIUE Faculty Research, Scholarship, and Creative Activity. 159.
Available for download on Monday, March 16, 2026