ON INFINITE SYSTEM OF RESONANCE AND EIGENVALUES WITH EXPONENTIAL ASYMPTOTICS GENERATED BY DISTANT PERTURBATIONS

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50017890" target="_blank" >RIV/62690094:18470/20:50017890 - isvavai.cz</a>

Result on the web

<a href="https://matem.anrb.ru/sites/default/files/files/vupe48/Borisov.pdf" target="_blank" >https://matem.anrb.ru/sites/default/files/files/vupe48/Borisov.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.13108/2020-12-4-3" target="_blank" >10.13108/2020-12-4-3</a>

Result language

angličtina

Original language name

ON INFINITE SYSTEM OF RESONANCE AND EIGENVALUES WITH EXPONENTIAL ASYMPTOTICS GENERATED BY DISTANT PERTURBATIONS

Original language description

We consider an one-dimensional Schrodinger operator with four distant potentials separated by large distance. All distances are proportional to a sam large parameter. The initial potentials are of kink shapes, which are glued mutually so that the final potential vanishes at infinity and between the second and third initial potentials and it is equal to one between the first and the second potentials as well as between the third and fourth potentials. The potentials are not supposed to be real and can be complex-valued. We show that under certain, rather natural and easily realizable conditions on the four initial potentials, the considered operator with distant potentials possesses infinitely many resonances and/or eigenvalues of form lambda - k(n)(2), n is an element of Z, which accumulate along a given segment in the essential spectrum. The distance between neighbouring numbers k(n) is of order the reciprocal of the distance between the potentials, while the imaginary parts of these quantities are exponentially small. For the numbers k(n) we obtain the representations via the limits of some explicitly calculated sequences and the sum of infinite series. We also prove explicit effective estimates for the convergence rates of the sequences and for the remainders of the series.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2020

Confidentiality

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

Name of the periodical

UFA MATHEMATICAL JOURNAL

ISSN

2074-1863

e-ISSN

—

Volume of the periodical

12

Issue of the periodical within the volume

4

Country of publishing house

RU - RUSSIAN FEDERATION

Number of pages

16

Pages from-to

3-18

UT code for WoS article

000607979900001

EID of the result in the Scopus database

—