Asymptotic formulae with remainder estimates for eigenvalue branches of the Schrödinger operator ![]() |
| |
Authors: | S Z Levendorskii |
| |
Institution: | Rostov Institute of National Economy, Engels'a 69, 344798, Rostov-on-Don, Russia |
| |
Abstract: | The Floquet theory provides a decomposition of a periodic Schrödinger operator into a direct integral, over a torus, of operators on a basic period cell. In this paper, it is proved that the same transform establishes a unitary equivalence between a multiplier by a decaying potential and a pseudo-differential operator on the torus, with an operator-valued symbol. A formula for the symbol is given. As applications, precise remainder estimates and two-term asymptotic formulas for spectral problems for a perturbed periodic Schrödinger operator are obtained. |
| |
Keywords: | |
|
| 点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息 |
| 点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文 |
|