The multiplication operator, zero location and asymptotic for non-diagonal Sobolev norms

14 pages, no figures.-- Online version published Jul 9, 2009.Article in press.In this paper we are going to study the zero location and asymptotic behavior of extremal polynomials with respect to a generalized non-diagonal Sobolev norm in which the product of the function and its derivative appears. The orthogonal polynomials with respect to this Sobolev norm are a particular case of those extremal polynomials. The multiplication operator by the independent variable is the main tool in order to obtain our results.Supported in part by three grants from M.E.C. (MTM 2006-13000-C03-02, MTM 2006-11976 and MTM 2007-30904-E) and by a grant from U.C.III M./C.A.M. (CCG07-UC3M/ESP-3339), Spain.Publicad