Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
We consider discrete Schrödinger operators with periodic potentials on periodic graphs perturbed by guided non-positive potentials, which are periodic in some directions and finitely supported in other ones. The spectrum of the unperturbed operator is a union of a finite number of non-degenerate bands and eigenvalues of infinite multiplicity. We show that the spectrum of the perturbed operator consists of the “unperturbed” one plus the additional guided spectrum, which is a union of a finite number of bands. We estimate the position of the guided bands and their length in terms of graph geometric parameters. We also determine the asymptotics of the guided bands for large guided potentials. Moreover, we show that the possible number of the guided bands, their length and position can be rather arbitrary for some specific potentials.
Язык оригинала | английский |
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Страницы (с-по) | 4869-4883 |
Число страниц | 15 |
Журнал | Proceedings of the American Mathematical Society |
Том | 145 |
Номер выпуска | 11 |
DOI | |
Состояние | Опубликовано - 1 янв 2017 |
ID: 35631589