Abstract
Consider a family of Sturm-Liouville operators H θ on the half-axis defined as
with the boundary condition
and the limit point case at infinity. We show that it is possible for all H θ to have dense absolutely continuous and dense singular spectrum. The construction is based on integral representations of Pick functions in the upper half-plane. We also discuss applications to the Krein spectral shift.
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del Rio, R., Fuentes, S., Poltoratski, A. (2002). Families of Spectral Measures with Mixed Types. In: Albeverio, S., Elander, N., Everitt, W.N., Kurasov, P. (eds) Operator Methods in Ordinary and Partial Differential Equations. Operator Theory: Advances and Applications, vol 132. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8219-4_12
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DOI: https://doi.org/10.1007/978-3-0348-8219-4_12
Publisher Name: Birkhäuser, Basel
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