Infinite-Dimensional Measure Spaces and Frame Analysis
arXiv:1606.04866
Abstract
We study certain infinite-dimensional probability measures in connection with frame analysis. Earlier work on frame-measures has so far focused on the case of finite-dimensional frames. We point out that there are good reasons for a sharp distinction between stochastic analysis involving frames in finite vs infinite dimensions. For the case of infinite-dimensional Hilbert space , we study three cases of measures. We first show that, for infinite dimensional, 1 one must resort to infinite dimensional measure spaces which properly contain . The three cases we consider are: (i) Gaussian frame measures, (ii) Markov path-space measures, and (iii) determinantal measures.
22 pages