TY - BOOK A1 - Witt, Ingo T1 - A calculus for a class of finitely degenerate pseudodifferential operators T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Witt, Ingo T1 - A calculus for a class of finitely degenerate pseudodifferential operators N2 - For a class of degenerate pseudodifferential operators, local parametrices are constructed. This is done in the framework of a pseudodifferential calculus upon adding conditions of trace and potential type, respectively, along the boundary on which the operators degenerate. T3 - Preprint - (2002) 05 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26246 ER - TY - BOOK A1 - Maniccia, L. A1 - Schulze, Bert-Wolfgang T1 - An algebra of meromorphic corner symbols T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Maniccia, L. A1 - Schulze, Bert-Wolfgang T1 - An algebra of meromorphic corner symbols N2 - Operators on manifolds with corners that have base configurations with geometric singularities can be analysed in the frame of a conormal symbolic structure which is in spirit similar to the one for conical singularities of Kondrat'ev's work. Solvability of elliptic equations and asymptotics of solutions are determined by meromorphic conormal symbols. We study the case when the base has edge singularities which is a natural assumption in a number of applications. There are new phenomena, caused by a specific kind of higher degeneracy of the underlying symbols. We introduce an algebra of meromorphic edge operators that depend on complex parameters and investigate meromorphic inverses in the parameter-dependent elliptic case. Among the examples are resolvents of elliptic differential operators on manifolds with edges. T3 - Preprint - (2002) 18 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26360 ER - TY - BOOK A1 - Tarkhanov, Nikolai Nikolaevich T1 - Anisotropic edge problems T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Tarkhanov, Nikolai Nikolaevich T1 - Anisotropic edge problems N2 - We investigate elliptic pseudodifferential operators which degenerate in an anisotropic way on a submanifold of arbitrary codimension. To find Fredholm problems for such operators we adjoint to them boundary and coboundary conditions on the submanifold.The algebra obtained this way is a far reaching generalisation of Boutet de Monvel's algebra of boundary value problems with transmission property. We construct left and right regularisers and prove theorems on hypoellipticity and local solvability. T3 - Preprint - (2002) 09 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26280 ER - TY - BOOK A1 - Harutjunjan, Gohar A1 - Schulze, Bert-Wolfgang T1 - Asymptotics and relative index on a cylinder with conical cross section T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Harutjunjan, Gohar A1 - Schulze, Bert-Wolfgang T1 - Asymptotics and relative index on a cylinder with conical cross section N2 - We study pseudodifferential operators on a cylinder IR x B with cross section B that conical singularities. Configurations of that kind are the local model of cornere singularities with base spaces B. Operators A in our calculus are assumed to have symbols α which are meromorphic in the complex covariable with values in the space of all cone operators on B. In case α is dependent of the axial variable t ∈ IR, we show an explicit formula for solutions of the homogeneous equation. Each non-bjectivity point of the symbol in the complex plane corresponds to a finite-dimensional space of solutions. Moreover, we give a relative index formula. T3 - Preprint - (2002) 27 KW - Meromorphic operator functions KW - relative index formulas KW - parameter-dependent cone operators Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26446 ER - TY - BOOK A1 - Davis, Simon T1 - Connections and generalized gauge transformation T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Davis, Simon T1 - Connections and generalized gauge transformations N2 - The derivation of the standard model from a higher-dimensional action suggests a further study of the fibre bundle formulation of gauge theories to determine the variations in the choice of structure group that are allowed in this geometrical setting. The action of transformations on the projection of fibres to their submanifolds are characteristic of theories with fewer gauge vector bosons, and specific examples are given, which may have phenomenological relevance. The spinor space for the three generations of fermions in the standard model is described algebraically. T3 - Preprint - (2002) 29 KW - bundles KW - connections KW - fibre coordinates KW - parallelizable spheres KW - division algebras KW - force unification Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26468 ER -