Spectral analysis of the diffusion operator with random jumps from the boundary

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F16%3A00466585" target="_blank" >RIV/61389005:_____/16:00466585 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00209-016-1677-y" target="_blank" >http://dx.doi.org/10.1007/s00209-016-1677-y</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00209-016-1677-y" target="_blank" >10.1007/s00209-016-1677-y</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Spectral analysis of the diffusion operator with random jumps from the boundary

Popis výsledku v původním jazyce

Using an operator-theoretic framework in a Hilbert-space setting, we perform a detailed spectral analysis of the one-dimensional Laplacian in a bounded interval, subject to specific non-self-adjoint connected boundary conditions modelling a random jump from the boundary to a point inside the interval. In accordance with previous works, we find that all the eigenvalues are real. As the new results, we derive and analyse the adjoint operator, determine the geometric and algebraic multiplicities of the eigenvalues, write down formulae for the eigenfunctions together with the generalised eigenfunctions and study their basis properties. It turns out that the latter heavily depend on whether the distance of the interior point to the centre of the interval divided by the length of the interval is rational or irrational. Finally, we find a closed formula for the metric operator that provides a similarity transform of the problem to a self-adjoint operator.

Název v anglickém jazyce

Spectral analysis of the diffusion operator with random jumps from the boundary

Popis výsledku anglicky

Using an operator-theoretic framework in a Hilbert-space setting, we perform a detailed spectral analysis of the one-dimensional Laplacian in a bounded interval, subject to specific non-self-adjoint connected boundary conditions modelling a random jump from the boundary to a point inside the interval. In accordance with previous works, we find that all the eigenvalues are real. As the new results, we derive and analyse the adjoint operator, determine the geometric and algebraic multiplicities of the eigenvalues, write down formulae for the eigenfunctions together with the generalised eigenfunctions and study their basis properties. It turns out that the latter heavily depend on whether the distance of the interior point to the centre of the interval divided by the length of the interval is rational or irrational. Finally, we find a closed formula for the metric operator that provides a similarity transform of the problem to a self-adjoint operator.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BE - Teoretická fyzika

OECD FORD obor

—

Projekt

<a href="/cs/project/GA14-06818S" target="_blank" >GA14-06818S: Rigorózní metody v kvantové dynamice: geometrie a magnetická pole</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

Mathematische Zeitschrift

ISSN

0025-5874

e-ISSN

—

Svazek periodika

284

Číslo periodika v rámci svazku

3-4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

24

Strana od-do

877-900

Kód UT WoS článku

000386769300008

EID výsledku v databázi Scopus

2-s2.0-84968616677