On a spectral theorem of Weyl

Nigel Higson; Qijun Tan

On a spectral theorem of Weyl

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arxiv 1611.03396 v3 pith:WZE7OD4G submitted 2016-11-10 math.OA math.CAmath.SP

Nigel Higson , Qijun Tan This is my paper · ORCID

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keywords weyloperatorstheoremanalysisasymptoticallybettercoefficientsconstant

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We give a geometric proof of a theorem of Weyl on the continuous part of the spectrum of Sturm-Liouville operators on the half-line with asymptotically constant coefficients. Earlier proofs due to Weyl and Kodaira depend on special features of Green's functions for linear ordinary differential operators; ours might offer better prospects for generalization to higher dimensions, as required for example in noncommutative harmonic analysis.

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Regular solutions of the hydrogen Schrödinger equation form an algebraic family of Harish-Chandra modules, and its Jantzen filtration recovers the physical spectrum and states.

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