an:01157098
Zbl 0914.58029
Schulze, Bert-Wolfgang; Sternin, Boris; Shatalov, Victor
An operator algebra on manifolds with cusp-type singularities
EN
Ann. Global Anal. Geom. 16, No. 2, 101-140 (1998).
00048175
1998
j
58J05 35J70 47A53
Fredholm theory; cusp-type singularities; pseudodifferential operators
The algebra of pseudodifferential operators on an arbitrary smooth manifold with a finite number of points of cusp-type is investigated. A family of local cusp algebras is constructed and the local Fredholm properties are established. The Fredholm property (global) is a direct consequence of the existence of local regularizers. The resurgent character of solutions is proved for elliptic pseudodifferential equations with infinitely many exponentially flat near-singular points on the right-hand side.
V.M.Deundjak (Rostov-na-Donu)