2 papers
math.FA2023
The Positive-Definite Completion Problem
Kartik G. Waghmare, Victor M. Panaretos
We study the positive-definite completion problem for kernels on a variety of domains and prove results concerning the existence, uniqueness, and characterization of solutions. In…
math.PR2023
A Karhunen-Loève Theorem for Random Flows in Hilbert spaces
Leonardo V. Santoro, Kartik G. Waghmare, Victor M. Panaretos
We develop a generalisation of Mercer's theorem to operator-valued kernels in infinite dimensional Hilbert spaces. We then apply our result to deduce a Karhunen-Loève theorem, vali…