On the asymptotically simplicity of periodic eigenvalues and Titchmarsh's formula

Alp Arslan Kıraç

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arXiv · 1407.4994

On the asymptotically simplicity of periodic eigenvalues and Titchmarsh's formula

Alp Arslan Kıraç

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Abstract

We consider Sturm-Liouville equation $y^{\prime\prime}+(\lambda-q)y=0$ where $q\in L^{1}[0,a]$. We obtain various conditions on the Fourier coefficients of q such that the periodic eigenvalues having the form given by Titchmarsh are asymptotically simple. Under these conditions, we give some asymptotic estimates for the spectral gaps.

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BibTeX RIS

Alp Arslan Kıraç. 2014-07-18. On the asymptotically simplicity of periodic eigenvalues and Titchmarsh's formula. https://arxiv.org/abs/1407.4994

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