Abstract

We study the behaviour of Laplace-type operators H on a complex vector bundle E → M in the adiabatic limit of the base space. This space is a fibre bundle M → B with compact fibres and the limit corresponds to blowing up directions perpendicular to the fibres by a factor 1/e. Under a gap condition on the fibre-wise eigenvalues we prove existence of effective operators that provide asymptotics to any order in e for H (with Dirichlet boundary conditions), on an appropriate almost-invariant subspace of L²(E).

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