An Inverse Spectral Problem for Non-Self-Adjoint Jacobi Matrices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F24%3A00372144" target="_blank" >RIV/68407700:21340/24:00372144 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1093/imrn/rnad314" target="_blank" >https://doi.org/10.1093/imrn/rnad314</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/imrn/rnad314" target="_blank" >10.1093/imrn/rnad314</a>

Result language
angličtina
Original language name
An Inverse Spectral Problem for Non-Self-Adjoint Jacobi Matrices
Original language description
We consider the class of bounded symmetric Jacobi matrices $J$ with positive off-diagonal elements and complex diagonal elements. With each matrix $J$ from this class, we associate the spectral data, which consists of a pair $(nu ,psi )$. Here $nu $ is the spectral measure of $|J|=sqrt {J<^>{*}J}$ and $psi $ is a phase function on the real line satisfying $|psi |leq 1$ almost everywhere with respect to the measure $nu $. Our main result is that the map from $J$ to the pair $(nu ,psi )$ is a bijection between our class of Jacobi matrices and the set of all spectral data.
Czech name
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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
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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