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Higher order deriviatives of heat semigroups on spheres and Riemannian symmetric space
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Elworthy, K. D. (2022) Higher order deriviatives of heat semigroups on spheres and Riemannian symmetric space. In: Ugolini , Stefania and Fuhrman , Marco and Mastrogiacomo , Elisa and Morando, Paola and Rüdiger, Barbara , (eds.) Geometry and Invariance in Stochastic Dynamics : Verona, Italy, March 25-29, 2019. Springer Proceedings in Mathematics & Statistics, 378 . Cham: Springer Nature, pp. 113-136. ISBN 9783030874315
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Official URL: https://doi.org/10.1007/978-3-030-87432-2_7
Abstract
As a very special case of a more general procedure a formula is derived for the Hessian of the solutions Ptf of the heat equation for functions on the sphere Sn . The formula demonstrates that for higher order derivatives there can be a spectrum of decay/growth rates, unlike the generic situation for first derivatives which is fundamental for Bakry-Emery theory. The method used is then applied for higher derivatives for spheres, and could be used for compact Riemannian symmetric spaces.
| Item Type: | Book Item | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Diffusion processes, Stochastic analysis, Riemannian manifolds, Symmetry (Mathematics) , Harmonic analysis, Homogeneous spaces | ||||||
| Series Name: | Springer Proceedings in Mathematics & Statistics | ||||||
| Journal or Publication Title: | Geometry and Invariance in Stochastic Dynamics | ||||||
| Publisher: | Springer Nature | ||||||
| Place of Publication: | Cham | ||||||
| ISBN: | 9783030874315 | ||||||
| Book Title: | Geometry and Invariance in Stochastic Dynamics : Verona, Italy, March 25-29, 2019 | ||||||
| Editor: | Ugolini , Stefania and Fuhrman , Marco and Mastrogiacomo , Elisa and Morando, Paola and Rüdiger, Barbara | ||||||
| Official Date: | 1 January 2022 | ||||||
| Dates: |
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| Volume: | 378 | ||||||
| Number of Pages: | 265 | ||||||
| Page Range: | pp. 113-136 | ||||||
| DOI: | 10.1007/978-3-030-87432-2_7 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Copyright Holders: | © Springer Nature Switzerland AG 2021 | ||||||
| Date of first compliant deposit: | 11 November 2020 | ||||||
| Conference Paper Type: | Paper | ||||||
| Type of Event: | Conference |
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