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

Alp Arslan Kıraç

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

Spectral Theory 2014-11-04 v2 Functional Analysis

Authors: Alp Arslan Kıraç

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.

Keywords

Sturm-Liouville equation periodic eigenvalues asymptotically simple Titchmarsh's formula Fourier coefficients spectral gaps

Cite

@article{arxiv.1407.4994,
  title  = {On the asymptotically simplicity of periodic eigenvalues and Titchmarsh's formula},
  author = {Alp Arslan Kıraç},
  journal= {arXiv preprint arXiv:1407.4994},
  year   = {2014}
}

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