Orthogonal polynomials. Fourier series in orthogonal polynomials. Trace formula and asymptotics of Forsythe determinant.

The following issues will be outlined:

• Systems of polynomials $\{ p_n (x) \}$ $(n\in\mathbb{Z}^+$) orthogonal to a measure and systems of Sobolev polynomials $\{ \hat q_n (x) \}$ $(n\in\mathbb{Z}^+$).
• Fourier series on systems $\{ p_n (x) \}$ and $\{ \hat q_n (x) \}$.
• Trace formula and asymptotics of the Forsythe determinant.