03942nam a22005055i 4500 978-3-319-68903-6 DE-He213 20210619110915.0 cr nn 008mamaa 171222s2017 gw | s |||| 0|eng d 9783319689036 978-3-319-68903-6 10.1007/978-3-319-68903-6 doi QA614-614.97 PBKS bicssc MAT034000 bisacsh PBKS thema 514.74 23 Güneysu, Batu. author. aut http://id.loc.gov/vocabulary/relators/aut Covariant Schrödinger Semigroups on Riemannian Manifolds [electronic resource] / by Batu Güneysu. 1st ed. 2017. Cham : Springer International Publishing : Imprint: Birkhäuser, 2017. XVIII, 239 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Operator Theory: Advances and Applications, 0255-0156 ; 264 Sobolev spaces on vector bundles -- Smooth heat kernels on vector bundles -- Basis differential operators on Riemannian manifolds -- Some specific results for the minimal heat kernel -- Wiener measure and Brownian motion on Riemannian manifolds -- Contractive Dynkin potentials and Kato potentials -- Foundations of covariant Schrödinger semigroups -- Compactness of resolvents for covariant Schrödinger operators -- L^p properties of covariant Schrödinger semigroups -- Continuity properties of covariant Schrödinger semigroups -- Integral kernels for covariant Schrödinger semigroup -- Essential self-adjointness of covariant Schrödinger semigroups -- Form cores -- Applications. This monograph discusses covariant Schrödinger operators and their heat semigroups on noncompact Riemannian manifolds and aims to fill a gap in the literature, given the fact that the existing literature on Schrödinger operators has mainly focused on scalar Schrödinger operators on Euclidean spaces so far. In particular, the book studies operators that act on sections of vector bundles. In addition, these operators are allowed to have unbounded potential terms, possibly with strong local singularities.  The results presented here provide the first systematic study of such operators that is sufficiently general to simultaneously treat the natural operators from quantum mechanics, such as magnetic Schrödinger operators with singular electric potentials, and those from geometry, such as squares of Dirac operators that have smooth but endomorphism-valued and possibly unbounded potentials. The book is largely self-contained, making it accessible for graduate and postgraduate students alike. Since it also includes unpublished findings and new proofs of recently published results, it will also be interesting for researchers from geometric analysis, stochastic analysis, spectral theory, and mathematical physics. Global analysis (Mathematics). Manifolds (Mathematics). Partial differential equations. Global Analysis and Analysis on Manifolds. https://scigraph.springernature.com/ontologies/product-market-codes/M12082 Partial Differential Equations. https://scigraph.springernature.com/ontologies/product-market-codes/M12155 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783319689029 Printed edition: 9783319689043 Printed edition: 9783319886787 Operator Theory: Advances and Applications, 0255-0156 ; 264 https://doi.org/10.1007/978-3-319-68903-6 ZDB-2-SMA ZDB-2-SXMS Mathematics and Statistics (SpringerNature-11649) Mathematics and Statistics (R0) (SpringerNature-43713)