Operators with Periodic Hamiltonian Flows in Domains with the Boundary

Abstract: We consider operators in the domains with the boundaries and derive sharp spectral asymptotics (containing non-Weyl correction) in the case when Hamiltonian flow is periodic. Even if operator is scalar but not second order (or even second-order but there is an inner boundary with both refraction and reflection present) Hamiltonian flow is branching on the boundary and the notion of periodicity becomes more complicated.

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20)

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