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arXiv · 1606.04866

Infinite-Dimensional Measure Spaces and Frame Analysis

Palle E. T. Jorgensen·Myung-Sin Song
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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 $\mathcal{H}$, we study three cases of measures. We first show that, for $\mathcal{H}$ infinite dimensional, 1 one must resort to infinite dimensional measure spaces which properly contain $\mathcal{H}$. The three cases we consider are: (i) Gaussian frame measures, (ii) Markov path-space measures, and (iii) determinantal measures.

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Palle E. T. Jorgensen, Myung-Sin Song. 2016-06-15. Infinite-Dimensional Measure Spaces and Frame Analysis. https://arxiv.org/abs/1606.04866

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