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Infinite-Dimensional Measure Spaces and Frame Analysis

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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.

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Authors and Affiliations

  1. Department of Mathematics, The University of Iowa, Iowa City, IA, 52242, USA

    Palle E. T. Jorgensen

  2. Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL, 62026, USA

    Myung-Sin Song

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  1. Palle E. T. Jorgensen
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  2. Myung-Sin Song
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Correspondence to Myung-Sin Song.

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Jorgensen, P.E.T., Song, MS. Infinite-Dimensional Measure Spaces and Frame Analysis. Acta Appl Math 155, 41–56 (2018). https://doi.org/10.1007/s10440-017-0144-z

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  • DOI: https://doi.org/10.1007/s10440-017-0144-z

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