On Nikishin systems with discrete components and weak asymptotics of multiple orthogonal polynomials Articles uri icon

publication date

  • September 2017

start page

  • 389

end page

  • 449

issue

  • 3

volume

  • 72

international standard serial number (ISSN)

  • 0036-0279

electronic international standard serial number (EISSN)

  • 1468-4829

abstract

  • This survey considers multiple orthogonal polynomials with respect to Nikishin systems generated by a pair (sigma(1), sigma(2)) of measures with unbounded supports (supp(sigma(1)). R+, supp(sigma(2)) subset of R-) and with sigma(2) discrete. A Nikishin-type equilibrium problem in the presence of an external field acting on R+ and a constraint on R- is stated and solved. The solution is used for deriving the contracted zero distribution of the associated multiple orthogonal polynomials. Bibliography: 56 titles.

keywords

  • hermite-pade approximants; multiple orthogonal polynomials; orthogonality with respect to a discrete measure; weak asymptotics; vector equilibrium problem; nikishin systems