This book presents original research results on pseudodifferential operators.
C*-algebras generated by pseudodifferential operators with piecewise smooth symbols on a smooth manifold are considered. For each algebra, all the equivalence classes of irreducible representations are listed; as a consequence, a criterion for a pseudodifferential operator to be Fredholm is stated, the topology on the spectrum is described, and a solving series is constructed.
Pseudodifferential operators on manifolds with edges are introduced, their properties are considered in details, and an algebra generated by the operators is studied.
An introductory chapter includes all necessary preliminaries from the theory of pseudodifferential operators and C*-algebras.

The book gives a detailed study of C*-algebras generated by pseudodifferential operators with discontinuos symbols Solving composition series are constructed for a number of C*-algebras spanned by pseudodifferential operators Pseudodifferential operators on manifolds with edges are defined and a calculus of their scalar symbols is developed

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