Ivrii, Victor 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]. Cited in 2 Documents MSC: 35P20 Asymptotic distributions of eigenvalues in context of PDEs 47F05 General theory of partial differential operators PDFBibTeX XMLCite \textit{V. Ivrii}, in: Journées ``Équations aux dérivées partielles'', Saint-Jean-de-Monts, France, 31 mai au 4 juin 1999. Exposés Nos. I--XIX (1999). Nantes: Université de Nantes. Exp. No. 5, 11 p. (1999; Zbl 1103.35353) Full Text: Numdam