In this announcement we report on a recent characterization of the spectrum of one-dimensional Schrodinger operators <$E H~=~- d sup 2 "/" dx sup 2~+~V> in <$E L sup 2 (bold roman R;~dx)> with quasi-periodic complex-valued algebro-geometric potentials V (i.e., potentials V which satisfy one (and hence infinitely many) equation(s) of the stationary Korteweg-de Vries (KdV) hierarchy) associated with non-singular hyperelliptic curves. It turns out the spectrum of H coincides with the conditional stability set of H and that it can explicitly be described in terms of the mean value of the inverse of the diagonal Green's function of H. As a result, the spectrum of H consists of finitely many simple analytic arcs and one semi-infinite simple analytic arc in the complex plane. Crossings as well as confluences of spectral arcs are possible and discussed as well. These results extend to the <$E L sup p (bold roman R;~dx)>-setting for <$E p~symbol <174>~[1,~inf)>.

Індекс рубрикатора НБУВ: В161.626.12 + В312.23

Рубрики:

Спектральна теорія

Солітони

Шифр НБУВ: Ж14648 Пошук видання у каталогах НБУВ 

---

  Якщо, ви не знайшли інформацію про автора(ів) публікації, маєте бажання виправити або відобразити більш докладну інформацію про науковців України запрошуємо заповнити "Анкету науковця"