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High energy asymptotics of the integrated density of states of almost periodic pseudo-differential operators

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Periodic and Ergodic Spectral Problems

The existence of complete asymptotic expansion for the integrated density of states in the high energy regime was long conjectured for periodic Schrdinger operators. I will discuss the history of the subject and present an eventual solution in the multidimensional situation. It turns out that the result applies to a big class of almost periodic pseudo-differential operators with smooth symbols. The proof is based on an application of the gauge transform discussed in the minicourse of A. Sobolev during the introductory workshop. The talk is based on a joint work with L. Parnovski and R. Shterenberg.

This talk is part of the Isaac Newton Institute Seminar Series series.

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