Topological Levinson's theorem for inverse square potentials: complex, infinite, but not exceptional

H. Inoue; S. Richard

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Topological Levinson's theorem for inverse square potentials: complex, infinite, but not exceptional

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arxiv 1810.11961 v1 pith:EO7OT3MT submitted 2018-10-29 math.SP math-phmath.MP

H. Inoue , S. Richard This is my paper

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In this review paper we carry on our investigations on Schroedinger operators with inverse square potentials on the half-line. Depending on several parameters, such operators possess either a finite number of complex eigenvalues, or an infinite one, but also some spectral singularities embedded in the continuous spectrum (exceptional situations). The spectral and the scattering theory for these operators is recalled, and new results for the exceptional cases are provided. Some index theorems in scattering theory are also developed, and explanations why these results can not be extended to the exceptional cases are provided.

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