Transformation Operators for Sturm-Liouville Operators with Singular Potentials

By Rostyslav Hryniv, Y. Mykytyuk. 2004

80 citations recorded by the source corpus.

We construct transformation operators for Sturm-Liouville operators with singular potentials from the space W−12(0,1) and show that these transformation operators naturally appear during factorisation of Fredholm operators of a special form. Some applications to the spectral analysis of Sturm-Liouville operators with singular potentials under consideration are also given.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/27c8f30c660d6916855fc9af1cc0f21c8f97121d

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In Applied Mathematics

1. Y. Mykytyuk
2. Rostyslav Hryniv

In Mathematical Physics

1. Y. Mykytyuk
2. Rostyslav Hryniv

Citations in the corpus

• Inverse spectral problems for Sturm–Liouville operators with singular potentials (2002, methodology): “The kernels kσ (x, y) and f (x, y) of the operators Kσ and F satisfy the following GLM equation for a.e. x, y with x > y: kσ (x, y) + f (x, y) + ∫ x 0 kσ (x, s) f (s, y) ds = 0.”