TY - THES A1 - Seiler, Jörg T1 - Pseudodifferential Calculus on Manifolds with Non-Compact Edges Y1 - 1997 CY - Potsdam ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Seiler, Jörg T1 - Edge operators with conditions of Toeplitz type N2 - Ellipticity of operators on a manifold with edges can be treated in the framework of a calculus of 2 X 2-block matrix operators with trace and potential operators on the edges. The picture is similar to the pseudodifferential analysis of boundary-value problems. The extra conditions satisfy an analogue of the Shapiro-Lopatinskij condition, provided a topological obstruction for the elliptic edge-degenerate operator in the upper left corner vanishes; this is an analogue of a condition of Atiyah and Bott in boundary-value problems. In general, however, we need global projection data, similarly to global boundary conditions, known for Dirac operators or other geometric operators. The present paper develops a new calculus with global projection data for operators on manifolds with edges. In particular, we show the Fredholm property in a suitable scale of spaces and construct parametrices within the calculus Y1 - 2006 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Seiler, Jörg T1 - Boundary value problems with global projection conditions N2 - Parametrices of elliptic boundary value problems for differential operators belong to an algebra of pseudodifferential operators with the transmission property at the boundary. However, generically, smooth symbols on a manifold with boundary do not have this property, and several interesting applications require a corresponding more general calculus. We introduce here a new algebra of boundary value problems that contains Shapiro-Lopatinskij elliptic as well as global projection conditions; the latter ones are necessary, if an analogue of the Atiyah-Bott obstruction does not vanish. We show that every elliptic operator admits (up to a stabilisation) elliptic conditions of that kind. Corresponding boundary value problems are then Fredholm in adequate scales of spaces. Moreover, we construct parametrices in the calculus. (C) 2003 Elsevier Inc. All rights reserved Y1 - 2004 SN - 0022-1236 ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Seiler, Jörg T1 - Pseudodifferential boundary value problems with global projection conditions T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Seiler, Jörg T1 - Edge operators with conditions of toeplitz type T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Seiler, Jörg T1 - Elliptic complexes on manifolds with boundary JF - The journal of geometric analysis N2 - We show that elliptic complexes of (pseudo) differential operators on smooth compact manifolds with boundary can always be complemented to a Fredholm problem by boundary conditions involving global pseudodifferential projections on the boundary (similarly as the spectral boundary conditions of Atiyah, Patodi, and Singer for a single operator). We prove that boundary conditions without projections can be chosen if, and only if, the topological Atiyah-Bott obstruction vanishes. These results make use of a Fredholm theory for complexes of operators in algebras of generalized pseudodifferential operators of Toeplitz type which we also develop in the present paper. KW - Elliptic complexes KW - Manifolds with boundary KW - Atiyah-Bott obstruction KW - Toeplitz-type pseudodifferential operators Y1 - 2018 U6 - https://doi.org/10.1007/s12220-018-0014-6 SN - 1050-6926 SN - 1559-002X VL - 29 IS - 1 SP - 656 EP - 706 PB - Springer CY - New York ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Seiler, Jörg T1 - The edge algebra structure of boundary value problems T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2001 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schrohe, Elmar A1 - Seiler, Jörg T1 - The resolvent of closed extensions of cone differential operators T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schrohe, Elmar A1 - Seiler, Jörg T1 - Ellipticity and invertibility in the cone algebra on Lp-Sobolev spaces T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 1999 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Lauter, Robert A1 - Seiler, Jörg T1 - Pseudodifferential analysis on manifolds with boundary - a comparsion of b-calculus and cone algebra T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 1999 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Kapanadze, David A1 - Schulze, Bert-Wolfgang A1 - Seiler, Jörg T1 - Operators with singular trace conditions on a manifold with edges T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2006 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Gil, J. B. A1 - Schulze, Bert-Wolfgang A1 - Seiler, Jörg T1 - Holomorphic operator-valued symbols for edgedegenerate pseudo-differential operators Y1 - 1997 ER - TY - JOUR A1 - Coriasco, S. A1 - Seiler, Jörg A1 - Schrohe, Elmar T1 - Differential operators on conic manifolds : maximal regularity and parabolic equations Y1 - 2001 ER - TY - BOOK A1 - Coriasco, S. A1 - Schrohe, Elmar A1 - Seiler, Jörg T1 - Bounded imaginary powers of differential operators on manifolds with conical singularities T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2001 SN - 1437-739X PB - Univ. CY - Potsdam ER -