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

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/61389005:_____/21:00539466

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GX20-17749X" target="_blank" >GX20-17749X: Nové výzvy pro spektrální teorii: geometrie, pokročilé materiály a komplexní pole</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Evolution Equations

ISSN

1424-3199

e-ISSN

1424-3202

Svazek periodika

21

Číslo periodika v rámci svazku

January

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

25

Strana od-do

1651-1675

Kód UT WoS článku

000604865300001

EID výsledku v databázi Scopus

2-s2.0-85098774553