Finite-dimensional Sturm-Liouville vessels and their tau functions (Q429734)

The author introduces a theory of a class of finite-dimensional vessels, a concept originating from the work of \textit{M. S. Livshits} [Soobshch. Akad. Nauk Gruz. SSR 91, 281--284 (1978; Zbl 0406.47001)]. His work may be considered as a first step toward analyzing and constructing Lax-Phillips scattering theory for Sturm-Liouville differential equations on the half axis \((0,\infty)\) with singularity at \(0\). The author also develops a rich and interesting theory of vessels with deep connections to the notion of \(\tau\) function, arising in nonlinear differential equations (LDE), and to the Galois differential theory for LDEs.