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Covariant Schrodinger semigroups on ...

Guneysu, Batu.

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Covariant Schrodinger semigroups on Riemannian manifolds

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Covariant Schrodinger semigroups on Riemannian manifolds/ by Batu Guneysu.
作者:	Guneysu, Batu.
出版者:	Cham :Springer International Publishing : : 2017.,
面頁冊數:	xviii, 239 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Riemannian manifolds. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-68903-6
ISBN:	9783319689036

Covariant Schrodinger semigroups on Riemannian manifolds
Guneysu, Batu.

Covariant Schrodinger semigroups on Riemannian manifolds[electronic resource] /by Batu Guneysu. - Cham :Springer International Publishing :2017. - xviii, 239 p. :ill., digital ;24 cm. - Operator theory: advances and applications,v.2640255-0156 ;. - Operator theory: advances and applications ;v.264..

This monograph discusses covariant Schrodinger 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 Schrodinger operators has mainly focused on scalar Schrodinger 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 Schrodinger 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 Since it also includes unpublished findings and new proofs of recently published results, it will also be interesting for researchers from geometric analysis, stochastic analysis, spectral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.

ISBN: 9783319689036

Standard No.: 10.1007/978-3-319-68903-6doiSubjects--Topical Terms:

540526
Riemannian manifolds.

LC Class. No.: QA649

Dewey Class. No.: 516.373

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520 $a This monograph discusses covariant Schrodinger 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 Schrodinger operators has mainly focused on scalar Schrodinger 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 Schrodinger 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.
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