Spectral analysis of the multi-dimensional diffusion operator with random jumps from the boundary

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F21%3A00346576" target="_blank" >RIV/68407700:21340/21:00346576 - isvavai.cz</a>
Alternative codes found
RIV/61389005:_____/21:00539466
Result on the web
<a href="https://doi.org/10.1007/s00028-020-00647-1" target="_blank" >https://doi.org/10.1007/s00028-020-00647-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00028-020-00647-1" target="_blank" >10.1007/s00028-020-00647-1</a>

Result language
angličtina
Original language name
Spectral analysis of the multi-dimensional diffusion operator with random jumps from the boundary
Original language description
We develop a Hilbert space approach to the diffusion process of the Brownian motion in a bounded domain with random jumps from the boundary introduced by Ben-Ari and Pinsky in 2007. The generator of the process is defined by a diffusion elliptic differential operator in the space of square-integrable functions, subject to non-self-adjoint and non-local boundary conditions expressed through a probability measure on the domain. We obtain an expression for the difference between the resolvent of the operator and that of its Dirichlet realization. We prove that the numerical range is the whole complex plane, despite the fact that the spectrum is purely discrete and is contained in a half plane. Furthermore, for the class of absolutely continuous probability measures with square-integrable densities we characterize the adjoint operator and prove that the system of root vectors is complete. Finally, under certain assumptions on the densities, we obtain enclosures for the non-real spectrum and find a sufficient condition for the nonzero eigenvalue with the smallest real part to be real. The latter supports the conjecture of Ben-Ari and Pinsky that this eigenvalue is always real.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GX20-17749X" target="_blank" >GX20-17749X: New challenges for spectral theory: geometry, advanced materials and complex fields</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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