Convergence of expansions for eigenfunctions and asymptotics of the spectral data of the Sturm-Liouville problem

A. A. Pahlevanyan

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arXiv · 1902.06594

Convergence of expansions for eigenfunctions and asymptotics of the spectral data of the Sturm-Liouville problem

A. A. Pahlevanyan

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Abstract

Uniform convergence of the expansion of an absolutely continuous function for eigenfunctions of the Sturm-Liouville problem $-y" + q \left( x \right) y = \mu y,$ $y \left(0\right)=0,$ $y\left( \pi \right)\cos \beta + y'\left( \pi \right)\sin \beta = 0,$ $\beta \in \left( 0, \pi \right)$ with summable potential $q \in L_{\mathbb{R}}^1 \left[0, \pi \right]$ is proved. This result is used to obtain more precise asymptotic formulae for eigenvalues and norming constants of this problem.

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BibTeX RIS

A. A. Pahlevanyan. 2019-02-18. Convergence of expansions for eigenfunctions and asymptotics of the spectral data of the Sturm-Liouville problem. https://arxiv.org/abs/1902.06594

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