The calculus of Volterra Mellin pseudodifferential operators with operator-valued symbols

• Main Author: Thomas Krainer
• Format: Others
• Language: English
• Published: Universität Potsdam 2001
• Subjects: Mathematics
• Online Access: http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26185; http://opus.kobv.de/ubp/volltexte/2008/2618/

We introduce the calculus of Mellin pseudodifferential operators parameters based on "twisted" operator-valued Volterra symbols as well aas the abstract Mellin calclus with holomorphic symbols. We establish the properties of the symblic and operational calculi, and we give and make use of explicit oscillatory integral formulas on the symbolic side, e. g., for the Leibniz-product, kernel cut-off, and Mellin quantization. Moreover, we introduce the notion of parabolicity for the calculi of Volterra Mellin operators, and construct Volterra parametrices for parabolic operators within the calculi.