Sobolev-type orthogonal polynomials on the unit circle

35 pages, no figures.-- MSC2000 codes: 42C05.MR#: MR1891026 (2003e:42037)Zbl#: Zbl 1033.42025This paper deals with polynomials orthogonal with respect to a Sobolev-type inner product $$ \langle f,g\rangle =\int_{-\pi}^\pi f(e^{i\theta}) \overline{g(e^{i\theta})} d\mu(e^{i\theta})\, + \, \bold{f}(c)A (\bold{g}(c))^H.$$ where μ is a positive Borel measure supported on [−π,π), A is a nonsingular matrix and 1. We denote f(c)=(f(c),f'(c),\dots,f^{(p)}(c)) and v^H the transposed conjugate of the vector v. We establish the connection of such polynomials with orthogonal polynomials on the unit circle with respect to the measure [see attached full-text file]. Finally, we deduce the relative asymptotics for both families of orthogonal polynomials.The work of the first author (F. Marcellán) was partially supported by D.G.E.S. of Spain under grant PB96-0120-C03-01. The work of the second author (L. Moral) was partially supported by P.A.I. 1997 (Universidad de Zaragoza) CIE-10.Publicad