An iterative approach to operators on manifolds with singularities

We establish elements of a new approach to ellipticity and parametrices within operator algebras on manifolds with higher singularities, only based on some general axiomatic requirements on parameter-dependent operators in suitable scales of spaes. The idea is to model an iterative process with new generations of parameter-dependent operator theories, together with new scales of spaces that satisfy analogous requirements as the original ones, now on a corresponding higher level. The "full" calculus involves two separate theories, one near the tip of the corner and another one at the conical exit to infinity. However, concerning the conical exit to infinity, we establish here a new concrete calculus of edge-degenerate operators which can be iterated to higher singularities.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Potsdam

Year

2010

Author dc:creator

• Abed, Jamil

Contributors dc:contributor

• Schulze, Bert-Wolfgang

• Pseudo-Differentialoperatoren
• kanten- und ecken-entartete Symbole
• Elliptizität
• Parametrices
• höhere Singularitäten
• Pseudo-differential operators
• edge- and corner-degenerate symbols
• ellipticity
• higher singularities

Statement dc:rights

• Creative Commons - Namensnennung, Nicht kommerziell, Weitergabe zu gleichen Bedingungen 3.0 Deutschland

Repository record source_url

https://publishup.uni-potsdam.de/frontdoor/index/index/docId/4317

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-potsdam:4317