Multiplicities of Eigenvalues of the Diffusion Operator with Random Jumps from the Boundary

Jun Yan; Guoliang Shi

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arXiv · 1802.00091

Multiplicities of Eigenvalues of the Diffusion Operator with Random Jumps from the Boundary

Jun Yan·Guoliang Shi

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Abstract

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 $\Delta(\lambda) $. This can be used to determine the multiplicities of eigenvalues for concrete operators.

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BibTeX RIS

Jun Yan, Guoliang Shi. 2018-01-31. Multiplicities of Eigenvalues of the Diffusion Operator with Random Jumps from the Boundary. https://arxiv.org/abs/1802.00091

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