On the strong asymptotics for Sobolev orthogonal polynomials on the circle
The authors prove Szegős's asymptotic theorem for the orthogonal polynomials with respect to a Sobolev inner product of the following type \[ \langle f(z),g(z)\rangle_s= \sum^p_{k=0} \int^{2\pi}_0 f^{(k)}(e^{i\theta})\overline{g^{(k)}(e^{i\theta})} d\mu_k(\theta),\quad z= e^{i\theta}, \] with \(\mu_k\), \(k= 0,1,\dots, p-1\), finite positive Borel measures on \([0,2\pi]\) and \(\mu_p\) a measure in the Szegő class.
scientific article; zbMATH DE number 1903848