Singular integral operators on non-compact manifolds and analysis on polyhedral domains

2004/02/19 by Nistor, Victor
#Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.math/0402322

Abstract

We review the definition of a Lie manifold (M, \VV) and the construction of the algebra Ψ\sp∞\sb\VV(M) of pseudodifferential operators on a Lie manifold (M, \VV). We give some concrete Fredholmness conditions for pseudodifferential operators in Ψ\sp∞\sb\VV(M) for a large class of Lie manifolds (M, \VV). These Fredholmness conditions have applications to boundary value problems on polyhedral domains and to non-linear PDEs on non-compact manifolds. As an application, we determine the spectrum of the Dirac operator on a manifold with multi-cylindrical ends.

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