Mixed Type Multiple Orthogonal Polynomials for Two Nikishin Systems Articles uri icon

publication date

  • October 2010

start page

  • 255

end page

  • 306

issue

  • 2

volume

  • 32

international standard serial number (ISSN)

  • 0176-4276

electronic international standard serial number (EISSN)

  • 1432-0940

abstract

  • We study the logarithmic and ratio asymptotics of linear forms constructed from a Nikishin system which satisfy orthogonality conditions with respect to a system of measures generated by a second Nikishin system. This construction combines type I and type II multiple orthogonal polynomials. The logarithmic asymptotics of the linear forms is expressed in terms of the extremal solution of an associated vector valued equilibrium problem for the logarithmic potential. The ratio asymptotics is described by means of a conformal representation of an appropriate Riemann surface of genus zero onto the extended complex plane.