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Regularized trace of the Sturm-Liouville operator with irregular boundary conditions. (English) Zbl 1171.34355

From the introduction: This paper deals with the eigenvalue problem for the Sturm-Liouville equation
\[ u''-q(x)u+\lambda u=0 \tag{1} \]
on the interval \((0,\pi)\) with the boundary conditions
\[ u'(0)+ (-1)^\theta u'(\pi)+ bu(\pi)=0, \qquad u(0)+ (-1)^{\theta+1} u(\pi)=0, \tag{2} \]
where \(b\) is a complex number, \(b\neq 0\), \(\theta=0,1\). The goal of this article is to calculate the first-order regularized trace for (1)–(2).

MSC:

34L05 General spectral theory of ordinary differential operators
34B24 Sturm-Liouville theory
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