Review of spectral theory
In this chapter we collect the results from spectral theory that will be used in the sequel, concentrating our attention on the spectral theory of Schrödinger operators on Riemannian manifolds. The vanishing and finite-dimensionality results which we will present in the next chapters are based on assumptions on the spectrum of suitable Schrödinger operators. And some of the geometric conditions which we will encounter in later chapters can be interpreted in spectral sense.
KeywordsWeak Solution Riemannian Manifold Quadratic Form Spectral Theory Discrete Spectrum
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