Applebaum, D. (2009) Some L2 properties of semigroups of measures on Lie groups. Semigroup Forum, 79 (2). pp. 217-228. ISSN 0037-1912
Abstract
We investigate the induced action of convolution semigroups of probability measures on Lie groups on the L 2-space of Haar measure. Necessary and sufficient conditions are given for the infinitesimal generator to be self-adjoint and the associated symmetric Dirichlet form is constructed. We show that the generated Markov semigroup is trace-class if and only if the measures have a square-integrable density. Two examples are studied in some depth where the spectrum can be explicitly computed, these being the n-torus and Riemannian symmetric pairs of compact type.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2009 Springer. This is an author produced version of a paper subsequently published in Semigroup Forum. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Lie group; Lie algebra; Convolution semigroup; Hunt semigroup; Hunt generator; Dirichlet form; Beurling-Deny representation; Trace-class operator; Hilbert-Schmidt operator; Lévy-Khinchine formula; Riemannian symmetric pairs; Spherical function; Subordinator |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Miss Anthea Tucker |
Date Deposited: | 30 Sep 2009 11:15 |
Last Modified: | 16 Nov 2015 11:48 |
Published Version: | http://dx.doi.org/10.1007/s00233-008-9130-0 |
Status: | Published |
Publisher: | Springer |
Refereed: | Yes |
Identification Number: | 10.1007/s00233-008-9130-0 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:9805 |