Kato's inequality and form boundedness of Kato potentials on arbitrary Riemannian manifolds

Let M be a Hermitian vector bundle with a Hermitian covariant derivative \nabla denote the Friedrichs extension of \nabla ^*\nabla /2 V:M\to \mathrm {End}(E) has a decomposition of the form V=V_1-V_2, V_1 \left \vert V_2 \right \vert, then one can define the form sum H(V):=H(0)\dotplus V \Gamma _{\m...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2014-04, Vol.142 (4), p.1289-1300
Main Author: Batu Güneysu
Format: Article
Language:English
Subjects:
Abstracting
Curvature
Mathematical inequalities
Mathematical theorems
Mathematical vectors
Radius of curvature
Riemann manifold
Scalars
Semigroups
Social classes
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Summary:Let M be a Hermitian vector bundle with a Hermitian covariant derivative \nabla denote the Friedrichs extension of \nabla ^*\nabla /2 V:M\to \mathrm {End}(E) has a decomposition of the form V=V_1-V_2, V_1 \left \vert V_2 \right \vert, then one can define the form sum H(V):=H(0)\dotplus V \Gamma _{\mathsf {L}^2}(M,E). Applications to quantum physics are discussed.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-2014-11859-4