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

  • Alexander Potrykus
DOI: https://doi.org/10.5209/rev_REMA.2009.v22.n1.16347
Keywords: Symbolic calculus, Non-smooth symbols, Negative definite functions, Feller semigroups

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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Published
2009-03-11
How to Cite
Potrykus A. . (2009). A Symbolic Calculus and a Parametrix Construction for Pseudodifferential Operators with Non-Smooth Negative Definite Symbols. Revista Matemática Complutense, 22(1), 187-207. https://doi.org/10.5209/rev_REMA.2009.v22.n1.16347
Issue
Vol. 22 No. 1 (2009)
Section
Articles

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