Criticality transition for positive powers of the discrete Laplacian on the half line

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F25%3A00379302" target="_blank" >RIV/68407700:21340/25:00379302 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4171/RMI/1523" target="_blank" >https://doi.org/10.4171/RMI/1523</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4171/RMI/1523" target="_blank" >10.4171/RMI/1523</a>

Result language
angličtina
Original language name
Criticality transition for positive powers of the discrete Laplacian on the half line
Original language description
We study the criticality and subcriticality of positive powers of the discrete Laplacian acting on positive integeres. We prove that these positive powers of the Laplacian are critical if and only if they are greater than or equal to 3/2. We complement our analysis with Hardy type inequalities in the subcritical regimes. As an illustration of the critical case, we describe the negative eigenvalues emerging by coupling the discrete bilaplacian with an arbitrarily small localized potential.
Czech name
—
Czech description
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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

Project
<a href="/en/project/GX20-17749X" target="_blank" >GX20-17749X: New challenges for spectral theory: geometry, advanced materials and complex fields</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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