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

DOI10.1090/S0002-9939-2014-11859-4zbMath1296.58023arXiv1105.0532OpenAlexW2964131334WikidataQ115289245 ScholiaQ115289245MaRDI QIDQ5401368

Batu Güneysu

Publication date: 13 March 2014

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.0532

zbMATH Keywords

Riemannian manifoldgeodesicsKato classquantum physicsFriedrichs extensions

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Linear symmetric and selfadjoint operators (unbounded) (47B25) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On generalized Schrödinger semigroups
• Coulomb systems on Riemannian manifolds and stability of matter
• The Feynman-Kac formula for Schrödinger operators on vector bundles over complete manifolds
• Kato class measures of symmetric Markov processes under heat kernel estimates
• ``Localized self-adjointness of Schrödinger type operators on Riemannian manifolds.
• Perturbation theory for linear operators.
• Perturbation of Dirichlet forms by measures
• Nonrelativistic hydrogen type stability problems on nonparabolic 3-manifolds
• Schrödinger operators with singular potentials
• Brownian motion and harnack inequality for Schrödinger operators
• THE KERNEL OF DIRAC OPERATORS ON ${\mathbb S}^3$ AND ℝ³
• Riemannian Geometry
• Heat equation derivative formulas for vector bundles

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