arXiv subjects

Alexey Tikhonov

Publications and source records attributed to Alexey Tikhonov.

39 records · Page 3Linked to original sources

arXiv2005

Factorizations and invariant subspaces for weighted Schur classes

We study factorizations of operator valued functions of weighted Schur classes over multiply-connected domains. There is a correspondence between functions from weighted Schur classes and so-called ``conservative curved'' systems introduced in the paper. We show that the fundamental relationship between invariant subspaces of the main operator of a conservative system and factorizations of the corresponding operator valued function of Schur class, which is well known in the case of the unit disk, can be extended to our case. We develop new notions and constructions and discuss changes that should be made to the standard theory to obtain desired generalization.

math.FA↗

arXiv2005

Self-adjointness of Cauchy singular integral operator

We extend Krupnik's criterion of self-adjointness of the Cauchy singular integral operator to the case of finitely connected domains. The main aim of the paper is to present a new approach for proof of the criterion.

math.FA↗

arXiv2005

Conservative curved systems and free functional model

We introduce conservative curved systems over multiply connected domains and study relationships of such systems with related notions of functional model, characteristic function, and transfer function. In contrast to standard theory for the unit disk, characteristic functions and transfer functions are essentially different objects. We study possibility to recover the characteristic function for a given transfer function. As the result we obtain the procedure to construct the functional model for a given conservative curved system. We employ the functional model to solve some problems in perturbation theory.

math.FA↗