Monotonicity and asymptotics of zeros of Sobolev type orthogonal polynomials: A general case Articles uri icon


  • Mello, V. Mirela
  • Rafaeli, R .Fernando

publication date

  • November 2012

start page

  • 1663

end page

  • 1671


  • 62

International Standard Serial Number (ISSN)

  • 0168-9274

Electronic International Standard Serial Number (EISSN)

  • 1873-5460


  • We investigate the location, monotonicity, and asymptotics of the zeros of the polynomials orthogonal with respect to the Sobolev type inner product < p, q > (lambda,c.j) = integral(b)(a) p(x)q(x)mu(x) + lambda p((j))(c)q((j))(c), where mu is a positive Borel measure, lambda >= 0, j is an element of Z(+), and c is not an element of (a, b). We prove that these zeros are monotonic function of the parameter A and establish their asymptotics when either lambda converges to zero or to infinity. The precise location of the extreme zeros is also analyzed.