My first papers were devoted to completion problems for operators in the spaces with indefinite metric.

Later, I have been actively involved in the research of Toeplitz and Wiener-Hopf operators, integral equations and their applications to boundary value problems, Szegö's limit theorems, models of statistical physics, and the finite section method. Some of my publications are devoted to abstract theory of operators on Hilbert spaces, in particular, to the spectrum assignment problem, properties of numerical ranges and numerical radii, sectorial operators, etc.

I would especially like to mention the spectral theory of Toeplitz operators with piecewise continuous symbols on the spaces with arbitrary Hunt-Muckenhoupt-Wheeden weights, and the factorization theory of almost periodic matrix functions. The latter theory led to several applications, in particular, to the Carathéodory-Toeplitz and Nehari extension problems, convolution type equations on finite intervals, and antennae theory.

Sometime I hope to write a more detailed version of this page. Meanwhile, you can take a look at my list of publications.

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