Quantum Strips in Higher Dimensions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F20%3A00534047" target="_blank" >RIV/61389005:_____/20:00534047 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/20:00343578
Result on the web
<a href="https://doi.org/10.7153/oam-2020-14-41" target="_blank" >https://doi.org/10.7153/oam-2020-14-41</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.7153/oam-2020-14-41" target="_blank" >10.7153/oam-2020-14-41</a>
Alternative languages
Result language
angličtina
Original language name
Quantum Strips in Higher Dimensions
Original language description
We consider the Dirichlet Laplacian in unbounded strips on ruled surfaces in any space dimension. We locate the essential spectrum under the condition that the strip is asymptotically flat. If the Gauss curvature of the strip equals zero, we establish the existence of discrete spectrum under the condition that the curve along which the strip is built is not a geodesic. On the other hand, if it is a geodesic and the Gauss curvature is not identically equal to zero, we prove the existence of Hardy-type inequalities. We also derive an effective operator for thin strips, which enables one to replace the spectral problem for the Laplace-Beltrami operator on the two-dimensional surface by a one-dimensional Schrodinger operator whose potential is expressed in terms of curvatures.nnIn the appendix, we establish a purely geometric fact about the existence of relatively parallel adapted frames for any curve under minimal regularity hypotheses.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA18-08835S" target="_blank" >GA18-08835S: Quantum mechanics with non-self-adjoint operators: transition from spectra to pseudospectra</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Operators and Matrices
ISSN
1846-3886
e-ISSN
—
Volume of the periodical
14
Issue of the periodical within the volume
3
Country of publishing house
HR - CROATIA
Number of pages
31
Pages from-to
635-665
UT code for WoS article
000576740400004
EID of the result in the Scopus database
2-s2.0-85096692089