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Spectral functions of a canonical system of 2n-th order. (Russian) Zbl 0718.34112

Summary: The set of pseudospectral functions of a canonical system of differential equations \(dW(x,\lambda)/dx=i\lambda JH(x)W(x,\lambda),\) \(W(0,\lambda)=E_{2n}\), is described, where \(0\leq x\leq \ell <\infty\), \(H(x)=H^*(x)\geq 0\), \(J=\left[ \begin{matrix} 0\\ E_ n\end{matrix} \begin{matrix} E_ n\\ 0\end{matrix} \right].\) In terms of the Hamiltonians H(x) conditions are given which guarantee that the pseudospectral functions are spectral ones.

MSC:

34L05 General spectral theory of ordinary differential operators
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