# zbMATH — the first resource for mathematics

Accurate spectral asymptotics for periodic operators. (English) Zbl 1103.35353
Proceedings of the conference on partial differential equations, Saint-Jean-de-Monts, France, May 31–June 4, 1999. Exp. Nos. I–XIX (1999). Nantes: Université de Nantes (ISBN 2-86939-146-3/pbk). Exp. No. 5, 11 p. (1999).
Summary: Asymptotics with sharp remainder estimates are recovered for the number $$N(\tau)$$ of eigenvalues of operator $$A(x,D)-tW(x,x)$$ crossing level $$E$$ as $$t$$ runs from 0 to $$\tau, \tau\to\infty$$. Here $$A$$ is a periodic matrix operator, matrix $$W$$ is positive, periodic with respect to the first copy of $$x$$ and decaying as the second copy of $$x$$ goes to infinity, and $$E$$ either belongs to a spectral gap of $$A$$ or is at one of its ends. These problems were first treated in papers of M. Sh. Birman, Birman and A. Laptev, and Birman and T. Suslina.
For the entire collection see [Zbl 0990.00047].

##### MSC:
 35P20 Asymptotic distributions of eigenvalues in context of PDEs 47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
Full Text: