Generalized Trace Formula for PolynomialsOrthogonal in Continuous-Discrete Sobolev Spaces

In continuous-discrete Sobolev spaces a generalized trace formula for orthogonal polynomials $\{\widehat{q}_n\}_{n=0}^\infty$ is obtained. The proof of this formula is based on the representation of the Fejér kernel for the system $\{\widehat{q}_n\}_{n=0}^\infty$. As a consequence, a generalized trace formula for Gegenbauer–Sobolev polynomials in a discrete Sobolev space is obtained.