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MULTIPLICITIES OF EIGENVALUES OF THE DIFFUSION OPERATOR WITH RANDOM JUMPS FROM THE BOUNDARY

Part of: Markov processes General theory of linear operators Ordinary differential operators

Published online by Cambridge University Press:  28 November 2018

JUN YAN Open the ORCID record for JUN YAN [Opens in a new window]  and
GUOLIANG SHI Open the ORCID record for GUOLIANG SHI [Opens in a new window]
JUN YAN*
Affiliation:
School of Mathematics, Tianjin University, Tianjin, 300354, PR China email [email protected]
GUOLIANG SHI
Affiliation:
School of Mathematics, Tianjin University, Tianjin, 300354, PR China email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

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This paper deals with a non-self-adjoint differential operator which is associated with a diffusion process with random jumps from the boundary. Our main result is that the algebraic multiplicity of an eigenvalue is equal to its order as a zero of the characteristic function $\unicode[STIX]{x1D6E5}(\unicode[STIX]{x1D706})$. This is a new criterion for determining the multiplicities of eigenvalues for concrete operators.

Keywords

diffusioneigenvaluenon-self-adjointmultiplicity

MSC classification

Primary: 34L15: Eigenvalues, estimation of eigenvalues, upper and lower bounds
Secondary: 47A10: Spectrum, resolvent 60J60: Diffusion processes
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 99 , Issue 1 , February 2019 , pp. 101 - 113
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

The work was done at the University of Vienna while the first author was visiting the Fakultät für Mathematik, supported by the China Scholarship Council. This research was also supported by the National Natural Science Foundation of China (Grant No. 11601372) and the Science and Technology Research Project of Higher Education in Hebei Province (Grant No. QN2017044).

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