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Infinite-Dimensional Measure Spaces and Frame Analysis
Journal article   Peer reviewed

Infinite-Dimensional Measure Spaces and Frame Analysis

Palle Jorgensen and Myung-Sin Song
Acta Applicandae Mathematicae, Vol.155(1), pp.41-56
06/2018
DOI: 10.1007/s10440-017-0144-z

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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 ℋ, we study three cases of measures. We first show that, for ℋ infinite dimensional, 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.
Mathematics Partial Differential Equations Frames Reproducing kernel Computational Mathematics and Numerical Analysis Calculus of Variations and Optimal Control; Optimization Probability Theory and Stochastic Processes Hilbert space Karhunen-Loève Applications of Mathematics

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