Journal article
Infinite-Dimensional Measure Spaces and Frame Analysis
Acta Applicandae Mathematicae, Vol.155(1), pp.41-56
06/2018
DOI: 10.1007/s10440-017-0144-z
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.
Details
- Title: Subtitle
- Infinite-Dimensional Measure Spaces and Frame Analysis
- Creators
- Palle Jorgensen - 0000 0004 1936 8294 grid.214572.7 Department of Mathematics The University of Iowa Iowa City IA 52242 USAMyung-Sin Song - 0000 0001 0816 4489 grid.263857.d Department of Mathematics and Statistics Southern Illinois University Edwardsville Edwardsville IL 62026 USA
- Resource Type
- Journal article
- Publication Details
- Acta Applicandae Mathematicae, Vol.155(1), pp.41-56
- DOI
- 10.1007/s10440-017-0144-z
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- Publisher
- Springer Netherlands; Dordrecht
- Language
- English
- Date published
- 06/2018
- Academic Unit
- Mathematics
- Record Identifier
- 9983985934302771
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