## Commuting non-selfadjoint operators. Open systems, and wave equations.(English)Zbl 07406132

In this paper, generalized open systems, conservation laws and matrix wave equations are studied. The author considers the case of commuting nonselfadjoint operators when $$n \geq 3$$ and one of them is a coupling of dissipative and antidissipative operators with real spectra. Then it is proved than that the input, output and state of generalized open system corresponding to the commutative regular colligation satisfy conservation law. The solutions of wave equation are obtained by means of Livšic nonselfadjoint operator theory. The obtained results in the paper can be used for solving boundary value problem for solutions of matrix wave equations in the case of different open systems, generated by appropriate couples triples of commuting operators.

### MSC:

 47B28 Nonselfadjoint operators 47B44 Linear accretive operators, dissipative operators, etc. 47A48 Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. 60G12 General second-order stochastic processes 47F05 General theory of partial differential operators
Full Text: