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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