Hilbert-Schmidt operators vs. integrable systems of elliptic Calogero-Moser type III: The Heun case.

Ruijsenaars, Simon N.M.

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Displaying similar documents to “Hilbert-Schmidt operators vs. integrable systems of elliptic Calogero-Moser type III: The Heun case.”

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This text contains a slightly expanded version of my 6 hour mini-course at the PDE-meeting in Évian-les-Bains in June 2009. The first part gives some old and recent results on non-self-adjoint differential operators. The second part is devoted to recent results about Weyl distribution of eigenvalues of elliptic operators with small random perturbations. Part III, in collaboration with B. Helffer, gives explicit estimates in the Gearhardt-Prüss theorem for semi-groups.

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Three methods for the study of the solvability of semilinear equations with noninvertible linear parts are compared: the alternative method, the continuation method of Mawhin and a new perturbation method [22]-[27]. Some extension of the last method and applications to differential equations in Banach spaces are presented.