Titlebook: Covariant Schrödinger Semigroups on Riemannian Manifolds; Batu Güneysu Book 2017 Springer International Publishing AG 2017 covariant Schrö

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,Foundations of Covariant Schrödinger Semigroups,..The following definitions will be very convenient in the sequel:...a) Let . be a smooth metric .-vector bundle. Then a Borel section . is called a . on ., if one has .. Here, . denotes the adjoint of the finite-dimensional linear operator. . with respect to the fixed metric on .

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,,,-properties of Covariant Schrödinger Semigroups,In this chapter, . . be an arbitrary covariant Schrödinger bundle..The aim of this chapter is to extend the L.-bounds for e. from Theorem IV.10 to arbitrary covariant Schr¨odinger semigroups, with an explicit quantitative control of the operator norms.

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,Essential Self-adjointness of Covariant Schrödinger Operators,In this chapter, . . ..

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Smooth Compactly Supported Sections as Form Core,Let . be an arbitrary covariant Schrödinger bundle and assume . to be .-decomposable.

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Applications,In this section, . = 3..The Kato–Simon inequality (or, to be precise, its consequence (VII.18) for the corresponding bottoms of spectra) is of fundamental importance in quantum mechanics: As we shall explain in a moment, it provides a mathematically rigorous proof of the following statement..

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Covariant Schrödinger Semigroups on Riemannian Manifolds

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