@book{RabinovichSchulzeTarchanov1997, author = {Rabinovich, Vladimir and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {A calculus of boundary value problems in domains with Non-Lipschitz singular points}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1997, 09}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {54 S.}, year = {1997}, language = {en} } @unpublished{RabinovichSchulzeTarkhanov1997, author = {Rabinovich, Vladimir and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {A calculus of boundary value problems in domains with Non-Lipschitz Singular Points}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24957}, year = {1997}, abstract = {The paper is devoted to pseudodifferential boundary value problems in domains with singular points on the boundary. The tangent cone at a singular point is allowed to degenerate. In particular, the boundary may rotate and oscillate in a neighbourhood of such a point. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to singular points.}, language = {en} } @article{FedosovSchulzeTarkhanov2001, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {A general index formula on toric manifolds with conical point}, year = {2001}, language = {en} } @unpublished{FedosovSchulzeTarkhanov1999, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {A general index formula on tropic manifolds with conical points}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25501}, year = {1999}, abstract = {We solve the index problem for general elliptic pseudodifferential operators on toric manifolds with conical points.}, language = {en} } @unpublished{SchulzeTarkhanov1998, author = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {A Lefschetz fixed point formula in the relative elliptic theory}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25159}, year = {1998}, abstract = {A version of the classical Lefschetz fixed point formula is proved for the cohomology of the cone of a cochain mapping of elliptic complexes. As a particular case we show a Lefschetz formula for the relative de Rham cohomology.}, language = {en} } @unpublished{NazaikinskiiSchulzeSterninetal.1997, author = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor}, title = {A Lefschetz fixed point theorem for manifolds with conical singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25073}, year = {1997}, abstract = {We establish an Atiyah-Bott-Lefschetz formula for elliptic operators on manifolds with conical singular points.}, language = {en} } @article{HedayatMahmoudiSchulze2018, author = {Hedayat Mahmoudi, Mahdi and Schulze, Bert-Wolfgang}, title = {A new approach to the second order edge calculus}, series = {Journal of pseudo-differential operators and applications}, volume = {9}, journal = {Journal of pseudo-differential operators and applications}, number = {2}, publisher = {Springer}, address = {Basel}, issn = {1662-9981}, doi = {10.1007/s11868-017-0191-2}, pages = {265 -- 300}, year = {2018}, abstract = {We establish essential steps of an iterative approach to operator algebras, ellipticity and Fredholm property on stratified spaces with singularities of second order. We cover, in particular, corner-degenerate differential operators. Our constructions are focused on the case where no additional conditions of trace and potential type are posed, but this case works well and will be considered in a forthcoming paper as a conclusion of the present calculus.}, language = {en} } @book{FedosovSchulzeTarchanov1998, author = {Fedosov, Boris V. and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {A remark on the index of symmetric operators}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1998, 04}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {12 S.}, year = {1998}, language = {en} } @unpublished{FedosovSchulzeTarkhanov1998, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {A remark on the index of symmetric operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25169}, year = {1998}, abstract = {We introduce a natural symmetry condition for a pseudodifferential operator on a manifold with cylindrical ends ensuring that the operator admits a doubling across the boundary. For such operators we prove an explicit index formula containing, apart from the Atiyah-Singer integral, a finite number of residues of the logarithmic derivative of the conormal symbol.}, language = {en} } @unpublished{SchulzeNazaikinskiiSternin1998, author = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir and Sternin, Boris}, title = {A semiclassical quantization on manifolds with singularities and the Lefschetz Formula for Elliptic Operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25296}, year = {1998}, abstract = {For general endomorphisms of elliptic complexes on manifolds with conical singularities, the semiclassical asymptotics of the Atiyah-Bott-Lefschetz number is calculated in terms of fixed points of the corresponding canonical transformation of the symplectic space.}, language = {en} }