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

  • JUN YAN (a1) and GUOLIANG SHI (a2)
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 $\unicode[STIX]{x1D6E5}(\unicode[STIX]{x1D706})$ . This is a new criterion for determining the multiplicities of eigenvalues for concrete operators.

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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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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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