L2 Properties of Lévy Generators on Compact Riemannian Manifolds
We consider isotropic Lévy processes on a compact Riemannian manifold, obtained from an R d -valued Lévy process through rolling without slipping. We prove that the Feller semigroups associated with these processes extend to strongly continuous contraction semigroups on L p , for 1 ≤ p < ∞ . When...
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| Veröffentlicht in: | Journal of theoretical probability 2021, Vol.34 (2), p.1029-1042 |
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| container_issue | 2 |
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| container_title | Journal of theoretical probability |
| container_volume | 34 |
| creator | Applebaum, David Brockway, Rosemary Shewell |
| description | We consider isotropic Lévy processes on a compact Riemannian manifold, obtained from an
R
d
-valued Lévy process through rolling without slipping. We prove that the Feller semigroups associated with these processes extend to strongly continuous contraction semigroups on
L
p
, for
1
≤
p
<
∞
. When
p
=
2
, we show that these semigroups are self-adjoint. If, in addition, the motion has a non-trivial Brownian part, we prove that the generator has a discrete spectrum of eigenvalues and that the semigroup is trace-class. |
| doi_str_mv | 10.1007/s10959-019-00980-3 |
| format | Article |
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R
d
-valued Lévy process through rolling without slipping. We prove that the Feller semigroups associated with these processes extend to strongly continuous contraction semigroups on
L
p
, for
1
≤
p
<
∞
. When
p
=
2
, we show that these semigroups are self-adjoint. If, in addition, the motion has a non-trivial Brownian part, we prove that the generator has a discrete spectrum of eigenvalues and that the semigroup is trace-class.</description><identifier>ISSN: 0894-9840</identifier><identifier>EISSN: 1572-9230</identifier><identifier>DOI: 10.1007/s10959-019-00980-3</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Eigenvalues ; Mathematics ; Mathematics and Statistics ; Probability Theory and Stochastic Processes ; Riemann manifold ; Semigroups ; Statistics ; Stochastic processes</subject><ispartof>Journal of theoretical probability, 2021, Vol.34 (2), p.1029-1042</ispartof><rights>The Author(s) 2020</rights><rights>The Author(s) 2020. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-p723-567ac08b2828004d9a0d52adb17559152f021241db9dfbccf68cfce82f339e513</cites><orcidid>0000-0002-4766-7537</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10959-019-00980-3$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10959-019-00980-3$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Applebaum, David</creatorcontrib><creatorcontrib>Brockway, Rosemary Shewell</creatorcontrib><title>L2 Properties of Lévy Generators on Compact Riemannian Manifolds</title><title>Journal of theoretical probability</title><addtitle>J Theor Probab</addtitle><description>We consider isotropic Lévy processes on a compact Riemannian manifold, obtained from an
R
d
-valued Lévy process through rolling without slipping. We prove that the Feller semigroups associated with these processes extend to strongly continuous contraction semigroups on
L
p
, for
1
≤
p
<
∞
. When
p
=
2
, we show that these semigroups are self-adjoint. If, in addition, the motion has a non-trivial Brownian part, we prove that the generator has a discrete spectrum of eigenvalues and that the semigroup is trace-class.</description><subject>Eigenvalues</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Probability Theory and Stochastic Processes</subject><subject>Riemann manifold</subject><subject>Semigroups</subject><subject>Statistics</subject><subject>Stochastic processes</subject><issn>0894-9840</issn><issn>1572-9230</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNpFkMFKxDAQhoMoWFdfwFPAc3SSNNvkuBRdhYoiew9pm0iX3aQmXcFH8jl8MaMVPAwDwzf_Dx9ClxSuKUB1kygooQjQPKAkEH6ECioqRhTjcIwKkKokSpZwis5S2kKmFECBVg3DzzGMNk6DTTg43Hx9vn_gtfU2minEfPO4DvvRdBN-GezeeD8Yjx-NH1zY9ekcnTizS_biby_Q5u52U9-T5mn9UK8aMlaME7GsTAeyZZJJgLJXBnrBTN_SSghFBXPAKCtp36retV3nlrJznZXMca6soHyBrubYMYa3g02T3oZD9LlRM8EqqXh-zxSfqTTGwb_a-E9R0D-q9KxKZ1X6V5Xm_BsrpluX</recordid><startdate>2021</startdate><enddate>2021</enddate><creator>Applebaum, David</creator><creator>Brockway, Rosemary Shewell</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>C6C</scope><orcidid>https://orcid.org/0000-0002-4766-7537</orcidid></search><sort><creationdate>2021</creationdate><title>L2 Properties of Lévy Generators on Compact Riemannian Manifolds</title><author>Applebaum, David ; Brockway, Rosemary Shewell</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p723-567ac08b2828004d9a0d52adb17559152f021241db9dfbccf68cfce82f339e513</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Eigenvalues</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Probability Theory and Stochastic Processes</topic><topic>Riemann manifold</topic><topic>Semigroups</topic><topic>Statistics</topic><topic>Stochastic processes</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Applebaum, David</creatorcontrib><creatorcontrib>Brockway, Rosemary Shewell</creatorcontrib><collection>Springer Nature OA Free Journals</collection><jtitle>Journal of theoretical probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Applebaum, David</au><au>Brockway, Rosemary Shewell</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>L2 Properties of Lévy Generators on Compact Riemannian Manifolds</atitle><jtitle>Journal of theoretical probability</jtitle><stitle>J Theor Probab</stitle><date>2021</date><risdate>2021</risdate><volume>34</volume><issue>2</issue><spage>1029</spage><epage>1042</epage><pages>1029-1042</pages><issn>0894-9840</issn><eissn>1572-9230</eissn><abstract>We consider isotropic Lévy processes on a compact Riemannian manifold, obtained from an
R
d
-valued Lévy process through rolling without slipping. We prove that the Feller semigroups associated with these processes extend to strongly continuous contraction semigroups on
L
p
, for
1
≤
p
<
∞
. When
p
=
2
, we show that these semigroups are self-adjoint. If, in addition, the motion has a non-trivial Brownian part, we prove that the generator has a discrete spectrum of eigenvalues and that the semigroup is trace-class.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10959-019-00980-3</doi><tpages>14</tpages><orcidid>https://orcid.org/0000-0002-4766-7537</orcidid><oa>free_for_read</oa></addata></record> |
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| ispartof | Journal of theoretical probability, 2021, Vol.34 (2), p.1029-1042 |
| issn | 0894-9840 1572-9230 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Eigenvalues Mathematics Mathematics and Statistics Probability Theory and Stochastic Processes Riemann manifold Semigroups Statistics Stochastic processes |
| title | L2 Properties of Lévy Generators on Compact Riemannian Manifolds |
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