Asymptotically Extremal Polynomials with Respect to Varying Weights and Application to Sobolev Orthogonality Articles uri icon

publication date

  • October 2008

start page

  • 480

end page

  • 488


  • 2


  • 346

International Standard Serial Number (ISSN)

  • 0022-247X

Electronic International Standard Serial Number (EISSN)

  • 1096-0813


  • We study the asymptotic behavior of the zeros of a sequence of polynomials whose weighted norms, with respect to a sequence of weight functions, have the same nth root asymptotic behavior as the weighted norms of certain extremal polynomials. This result is applied to obtain the (contracted) weak zero distribution for orthogonal polynomials with respect to a Sobolev inner product with exponential weights of the form e−phi(x), giving a unified treatment for the so-called Freud (i.e., when phi has polynomial growth at infinity) and Erdös (when phi grows faster than any polynomial at infinity) cases. In addition, we provide a new proof for the bound of the distance of the zeros to the convex hull of the support for these Sobolev orthogonal polynomials.