2016/06/15 by Jorgensen, Palle E. T., Song, Myung-Sin
#46L60 #46L89 #47S50 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 42C40
paper · doi:10.48550/arxiv.1606.04866
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 H, we study three cases of measures. We first show that, for H infinite dimensional, 1 one must resort to infinite dimensional measure spaces which properly contain H. The three cases we consider are: (i) Gaussian frame measures, (ii) Markov path-space measures, and (iii) determinantal measures.