Spectral functions of subordinate Brownian motion on closed manifolds

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Abstract

For a class of subordinators, we investigate the spectrum of the infinitesimal generator of subordinate Brownian motion on a closed manifold. We consider three spectral functions of the generator: the zeta function, the heat trace and the spectral action. Each spectral function explicitly yields both probabilistic and geometric information, the latter through the classical heat invariants. All constructions are done with classical pseudodifferential operators and are fully analytically tractable.
Original languageEnglish
Pages (from-to)703-720
Number of pages18
JournalJournal of the London Mathematical Society
Volume93
Early online date27 Apr 2016
DOIs
StatePublished - Jun 2016

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Spectral function
Brownian motion
Heat
Closed
Brownian movement
Subordinator
Infinitesimal generator
Pseudodifferential operators
Riemann zeta function
Trace
Generator
Invariant

Cite this

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abstract = "For a class of subordinators, we investigate the spectrum of the infinitesimal generator of subordinate Brownian motion on a closed manifold. We consider three spectral functions of the generator: the zeta function, the heat trace and the spectral action. Each spectral function explicitly yields both probabilistic and geometric information, the latter through the classical heat invariants. All constructions are done with classical pseudodifferential operators and are fully analytically tractable.",
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AB - For a class of subordinators, we investigate the spectrum of the infinitesimal generator of subordinate Brownian motion on a closed manifold. We consider three spectral functions of the generator: the zeta function, the heat trace and the spectral action. Each spectral function explicitly yields both probabilistic and geometric information, the latter through the classical heat invariants. All constructions are done with classical pseudodifferential operators and are fully analytically tractable.

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