2009•Revista Matemática ComplutenseOpen access

A Symbolic Calculus and a Parametrix Construction for Pseudodifferential Operators with Non-Smooth Negative Definite Symbols

Alexander Potrykus

Abstract

We consider pseudodifferential operators that have non-smooth negative definite symbols and develop a corresponding symbolic calculus. Combining this symbolic calculus with the use of non-smooth symbols that are asymptotically constant in the co-variable we succeed infunding a parametrix for a certain pseudodifferential equation. This in turn allows us to show that some pseudodifferential operators with non-smooth negative definite symbols are pregenerators of Feller semigroups.

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Key concepts: Parametrix, Pseudodifferential operators, Mathematics, Variable (mathematics), Operator theory, Maple, Constant (computer programming), Pure mathematics