07-30 Vladimir Ryzhov

Functional Model of a Closed Non-Selfadjoint Operator (447K, pdf) Feb 2, 07

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Abstract. We construct the symmetric functional model for an arbitrary closed operator with a non-empty resolvent set acting on a separable Hilbert space. The main techniques of the study are based on the explicit form of the Sz.-Nagy-Foias model for a closed dissipative operator, the Potapov-Ginzburg transform of characteristic functions, and certain resolvent identities. All considerations are carried out under minimal assumptions, and obtained results are directly applicable to problems typically arising in mathematical physics. Explicit formulae for all objects relevant to the model construction are provided.

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