Spectral and pseudospectral functions of Hamiltonian systems: development of the results by Arov-Dym and Sakhnovich
DOI:
Keywords:
Hamiltonian system, spectral function, pseudospectral function, Fourier transform, $m$-functionAbstract
The main object of the paper is a Hamiltonian system $J y'-B(t)y=\lambda\Delta(t) y$ defined on an interval $[a,b) $ with the regular endpoint $a$. We define a pseudo\-spectral function of a singular system as a matrix-valued distribution function such that the generalized Fourier transform is a partial isometry with the minimally possible kernel. Moreover, we parameterize all spectral and pseudospectral functions of a given system by means of a Nevanlinna boundary parameter. The obtained results develop the results by Arov-Dym and Sakhnovich in this direction.References
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