Multi-operator colligations and multivariate characteristic functions. (English) Zbl 1253.47009
Summary: In the spectral theory of non-self-adjoint operators, there is a well-known operation of product of operator colligations. Many similar operations appear in the theory of infinite-dimensional classical groups as multiplications of double cosets. We construct characteristic functions for such double cosets and get semigroups of inner matrix-valued functions in matrix balls.
MSC:
| 47A48 | Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. |
| 20E99 | Structure and classification of infinite or finite groups |
Keywords:
non-selfadjoint operators; product of operator colligations; double cosets; characteristic functionsReferences:
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