Concerning asymptotic behavior for extremal polynomials associated to nondiagonal Sobolev norms Articles uri icon

publication date

  • January 2013

start page

  • 1

end page

  • 11

issue

  • 628031

volume

  • 2013

international standard serial number (ISSN)

  • 0972-6802

electronic international standard serial number (EISSN)

  • 1758-4965

abstract

  • Let P be the space of polynomials with complex coefficients endowed with a nondiagonal Sobolev norm parallel to .parallel to(1,p)(W)((V mu)), where the matrix V and the measure mu constitute a p- admissible pair for 1 <= p <= infinity. In this paperwe establish the zero location and asymptotic behavior of extremal polynomials associated to parallel to .parallel to(1,p)(W)((V mu)), stating hypothesis on the matrix V rather than on the diagonal matrix appearing in its unitary factorization.

keywords

  • orthogonal polynomials; multiplication operator; zero location; complex-plane; spaces; respect; curves