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Description of  Covariant Schrodinger Semigroups on Riemannian Manifolds (Operator Theory: Advances and Applications)

This monograph discusses covariant Schrdinger 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 Schrdinger operators has mainly focused on scalar Schrdinger 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 Schrdinger 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 Since it also includes unpublished findings and new proofs of recently published results, it will also be interesting for researchers from geometric analysis, stochastic analysis, spectral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. Please If You Want To Support Me Kindly Purchase Premium From Any Of My Download Links Thanks For Supporting Me And Purchasing Premium From My Links