Pseudodifferential operators on a class of noncompact manifolds

This paper introduces a new class of pseudodifferential (p.d.) operators acting in spaces of Bessel potentials of section-distributions over a noncompact (in the usual sense) manifold $M$ compactified by a set of points at infinity. Two-sided $L_p$ bounds are given for the factor-norm of a p.d. operator in the subspace of compact operators using the norm of its symbol. Necessary and sufficient conditions are given for the operators to be Noetherian, and well-posed problems are investigated on manifolds of the above structure with noncompact boundary.
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