Spectral properties of some differential operators of Sturm-Liouville type with homogeneous delay

Abstract

In this paper we observe the operator $ D^{2}=D^{2}(h,H,q,\alpha)$, $h, H\in \overline{\mathbb{R}}=\mathbb{R}\cup \{-\infty,\infty\}$, $q(x)\in L_{2}\left[0,\pi \right]$, $\alpha\in (0,1) $ and construct and partially transform its characteristic function. Those transformations enable more complete asymptotic decomposition of the zeroes and eigenvalues of the operator.

The goal of this paper is to contribute to the development of the spectral theory of differential operators with homogeneous delay.

Keywords

• characteristic function
• asymptotics
• homogenus delay

References

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