Abstract
In this paper we consider the problem of building the spectral function of a canonical differential equation when the potential is given. We restrict ourselves to the case where the spectral function is rational. An algorithm is proposed which allows the construction of the spectral function from the values of the potential and of a number of its derivatives at the origin. The approach is based on the solution of the partial realization problem for systems.
Dedicated to the memory of I.M. Glazman
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Alpay, D., Gohberg, I. (1997). Potentials Associated to Rational Weights. In: Gohberg, I., Lyubich, Y. (eds) New Results in Operator Theory and Its Applications. Operator Theory: Advances and Applications, vol 98. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8910-0_3
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DOI: https://doi.org/10.1007/978-3-0348-8910-0_3
Publisher Name: Birkhäuser, Basel
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