Abstract
We put forward a new transformation of the half-line Sturm-Liouville equation with non-smooth potentials from L p ,with p ≥ 2. This transformation yields existence of the Weyl solution with higher order WKB-type asymptotic behavior (spatial and spectral parameter). We apply our approach to the study of high-energy asymptotics for the Titchmarsh-Weyl m-function, improving on some relevant results of others.
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Rybkin, A. (2004). On a Transformation of the Sturm-Liouville Equation with Slowly Decaying Potentials and the Titchmarsh-Weyl m-function. In: Janas, J., Kurasov, P., Naboko, S. (eds) Spectral Methods for Operators of Mathematical Physics. Operator Theory: Advances and Applications, vol 154. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7947-7_13
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DOI: https://doi.org/10.1007/978-3-0348-7947-7_13
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