Functional Analysis and Applications Seminar 

03/02/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building
Vladimir Mityushev, Pedagogical Academy, Krakow, Poland

Constructive solution to the $C$-linear problem with piece-wise constant matrices

The $C$-linear conjugation problem with a piece-wise constant matrix $G(t)$ given on the real axis and discontinuous at the finite numbers of the points $W$ is stated as follows. To find a vector-function $F(z)$ analytic in the upper and lower half planes continuous in the closures of the half planes except the set $W$ where $F(t)$ is bounded. The upper and lower limit values of $F(t)$ on the real axis are linearly related via $G(t)$. A polynomial growth of $F(z)$ at infinity is admitted. This problem is solved in closed form by application of the functional equations method under some restrictions on the dimension of $F(z)$ and $\#W$.