Construction of self-adjoint differential operators with prescribed spectral properties
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F22%3A50019218" target="_blank" >RIV/62690094:18470/22:50019218 - isvavai.cz</a>
Result on the web
<a href="https://onlinelibrary.wiley.com/doi/10.1002/mana.201900491" target="_blank" >https://onlinelibrary.wiley.com/doi/10.1002/mana.201900491</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mana.201900491" target="_blank" >10.1002/mana.201900491</a>
Alternative languages
Result language
angličtina
Original language name
Construction of self-adjoint differential operators with prescribed spectral properties
Original language description
In this expository article some spectral properties of self-adjoint differential operators are investigated. The main objective is to illustrate and (partly) review how one can construct domains or potentials such that the essential or discrete spectrum of a Schrodinger operator of a certain type (e.g. the Neumann Laplacian) coincides with a predefined subset of the real line. Another aim is to emphasize that the spectrum of a differential operator on a bounded domain or bounded interval is not necessarily discrete, that is, eigenvalues of infinite multiplicity, continuous spectrum, and eigenvalues embedded in the continuous spectrum may be present. This unusual spectral effect is, very roughly speaking, caused by (at least) one of the following three reasons: The bounded domain has a rough boundary, the potential is singular, or the boundary condition is nonstandard. In three separate explicit constructions we demonstrate how each of these possibilities leads to a Schrodinger operator with prescribed essential spectrum.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematische Nachrichten
ISSN
0025-584X
e-ISSN
1522-2616
Volume of the periodical
295
Issue of the periodical within the volume
6
Country of publishing house
DE - GERMANY
Number of pages
33
Pages from-to
1063-1095
UT code for WoS article
000791828800001
EID of the result in the Scopus database
2-s2.0-85129456788