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Pseudodifferential Operators on Stratified Manifolds

V. Nazaikinskii·A. Savin·B. Sternin
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Abstract

We consider a specific class of manifolds with singularities, namely, stratified manifolds, and describe a class of pseudodifferential operators (PsiDO) related to differential operators with degeneration of first-order with respect to the distance to the strata on such manifolds. (For manifolds with isolated singularities, this is a Fuchs type degeneration.) We restrict ourselves to the case of zero-order operators in L^2 spaces. The definition of PsiDO adopted in our approach uses induction over the number of strata in the manifold. The induction process naturally involves PsiDO with parameters.

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V. Nazaikinskii, A. Savin, B. Sternin. 2005-12-01. Pseudodifferential Operators on Stratified Manifolds. https://arxiv.org/abs/math/0512025

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