17 citations · 101 across the 37 of their papers we have counts for
37 papers
New boundaries for positive definite functions
Palle Jorgensen, Feng Tian
With view to applications in stochastic analysis and geometry, we introduce a new correspondence for positive definite kernels (p.d.) and their associated reproducing kernel Hi…
An Infinite Dimensional Analysis of Kernel Principal Components
Palle E. T. Jorgensen, Sooran Kang, Myung-Sin Song +1
We study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kern…
Superposition, reduction of multivariable problems, and approximation
Palle Jorgensen, Feng Tian
We study reduction schemes for functions of "many" variables into system of functions in one variable. Our setting includes infinite-dimensions. Following Cybenko-Kolmogorov, the o…
Decomposition of Gaussian processes, and factorization of positive definite kernels
Palle Jorgensen, Feng Tian
We establish a duality for two factorization questions, one for general positive definite (p.d) kernels , and the other for Gaussian processes, say . The latter notion, for G…
On reproducing kernels, and analysis of measures
Palle Jorgensen, Feng Tian
Starting with the correspondence between positive definite kernels on the one hand and reproducing kernel Hilbert spaces (RKHSs) on the other, we turn to a detailed analysis of ass…
Martin boundaries of representations of the Cuntz algebra
Palle Jorgensen, Feng Tian
In a number of recent papers, the idea of generalized boundaries has found use in fractal and in multiresolution analysis; many of the papers having a focus on specific examples. P…