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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

—

Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BE - Theoretical physics

OECD FORD branch

—

Project

<a href="/en/project/GA14-06818S" target="_blank" >GA14-06818S: Rigorous Methods in Quantum Dynamics: Geometry and Magnetic Fields</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2016

Confidentiality

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

Name of the periodical

Mathematische Zeitschrift

ISSN

0025-5874

e-ISSN

—

Volume of the periodical

284

Issue of the periodical within the volume

3-4

Country of publishing house

DE - GERMANY

Number of pages

24

Pages from-to

877-900

UT code for WoS article

000386769300008

EID of the result in the Scopus database

2-s2.0-84968616677