Abstract
We consider self-adjoint Sturm-Liouville problems of the form Lu = λg(x)u, where L is an ordinary differential operator of order 2m, defined on the interval (0,1), and g is a real-valued function assuming both positive and negative values. For our problem, we prove under some assumptions that the eigenvectors and associated vectors constitute a Riesz basis in the space L 2 with the weight |g|. To study the problem, we consider the question of interpolation of some Sobolev spaces with weight.
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Pyatkov, S.G. (1998). Interpolation of some function spaces and indefinite Sturm-Liouville problems. In: Gohberg, I., Mennicken, R., Tretter, C. (eds) Differential and Integral Operators. Operator Theory: Advances and Applications, vol 102. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8789-2_14
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DOI: https://doi.org/10.1007/978-3-0348-8789-2_14
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