OPERATOR GROUP GENERATED BY A ONE-DIMENSIONAL DIRAC SYSTEM
- Authors: Savchuk A.M.1, Sadovnichaya I.V.1
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Affiliations:
- Lomonosov Moscow State University
- Issue: Vol 514, No 1 (2023)
- Pages: 79-81
- Section: МАТЕМАТИКА
- URL: https://journals.rcsi.science/2686-9543/article/view/247092
- DOI: https://doi.org/10.31857/S2686954323600568
- EDN: https://elibrary.ru/CZLLLF
- ID: 247092
Cite item
Abstract
In this paper, we construct a strongly continuous operator group generated by a one-dimensional Dirac operator acting in the space \(\mathbb{H} = {{\left( {{{L}_{2}}[0,\pi ]} \right)}^{2}}\). The potential is assumed to be summable. It is proved that this group is well-defined in the space \(\mathbb{H}\) and in the Sobolev spaces \(\mathbb{H}_{U}^{\theta }\), \(\theta > 0\), with fractional index of smoothness \(\theta \) and under boundary conditions \(U\). Similar results are proved in the spaces \({{\left( {{{L}_{\mu }}[0,\pi ]} \right)}^{2}}\), \(\mu \in (1,\infty )\). In addition we obtain estimates for the growth of the group as \(t \to \infty \).
Keywords
About the authors
A. M. Savchuk
Lomonosov Moscow State University
Author for correspondence.
Email: savchuk@cosmos.msu.ru
Russian Federation, Moscow
I. V. Sadovnichaya
Lomonosov Moscow State University
Author for correspondence.
Email: ivsad@yandex.ru
Russian Federation, Moscow
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