Journal article
Positive definite kernels and boundary spaces
Advances in operator theory, Vol.1(1), pp.123-133
12/01/2016
DOI: 10.22034/aot.1610.1044
Abstract
We consider a kernel based harmonic analysis of "boundary," and boundary representations. Our setting is general: certain classes of positive definite kernels. Our theorems extend (and are motivatedby) results and notions from classical harmonic analysis on the disk. Our positive definite kernels include those defined on infinite discrete sets, for example sets of vertices in electrical networks, or discrete sets which arise from sampling operations performed on positive definite kernels in a continuous setting. ¶ Below we give a summary of main conclusions in the paper: Starting with a given positive definite kernel $K$ we make precise generalized boundaries for $K$. They are measure theoretic "boundaries." Using the theory of Gaussian processes, we show that there is always such a generalized boundary for any positive definite kernel.
Details
- Title: Subtitle
- Positive definite kernels and boundary spaces
- Creators
- Palle JorgensenFeng Tian
- Resource Type
- Journal article
- Publication Details
- Advances in operator theory, Vol.1(1), pp.123-133
- Publisher
- Tusi Mathematical Research Group
- DOI
- 10.22034/aot.1610.1044
- ISSN
- 2538-225X
- eISSN
- 2538-225X
- Language
- English
- Date published
- 12/01/2016
- Academic Unit
- Mathematics
- Record Identifier
- 9984241160202771
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