Strong asymptotics for the Pollaczek multiple orthogonal polynomials

@article{Aptekarev2014StrongAF,
  title={Strong asymptotics for the Pollaczek multiple orthogonal polynomials},
  author={Alexander I. Aptekarev and Guillermo L{\'o}pez Lagomasino and Andrei Mart{\'i}nez-Finkelshtein},
  journal={Doklady Mathematics},
  year={2014},
  volume={92},
  pages={709-713}
}
The asymptotic properties of multiple orthogonal polynomials with respect to two Pollaczek weights with different parameters are considered. This set of weights is a Nikishin system generated by two measures with unbounded supports; moreover, the second measure is discrete. During the last years, multiple orthogonal polynomials with respect to Nikishin systems of this type have found wide applications in the theory of random matrices. Strong asymptotic formulas for the polynomials under… 

References

SHOWING 1-10 OF 49 REFERENCES

Generalized Pollaczek polynomials

For multiple orthogonal polynomials with respect to two Pollaczek weight functions weak asymptotics are obtained. It is shown that a solution of a vector equilibrium problem of the theory of

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

This survey considers multiple orthogonal polynomials with respect to Nikishin systems generated by a pair of measures with unbounded supports (, ) and with discrete. A Nikishin-type equilibrium

Extremal Polynomials on Discrete Sets

We study asymptotics for orthogonal polynomials and other extremal polynomials on infinite discrete sets, typical examples being the Meixner polynomials and the Charlier polynomials. Following ideas

On multiple orthogonal polynomials for discrete Meixner measures

The paper examines two examples of multiple orthogonal polynomials generalizing orthogonal polynomials of a discrete variable, meaning thereby the Meixner polynomials. One example is bound up with a

Nikishin Systems Are Perfect

K. Mahler introduced the concept of perfect systems in the general theory he developed for the simultaneous Hermite–Pade approximation of analytic functions. We prove that Nikishin systems are

Hermite-Padé approximations and multiple orthogonal polynomial ensembles

This paper is concerned with Hermite-Padé rational approximants of analytic functions and their connection with multiple orthogonal polynomial ensembles of random matrices. Results on the analytic

A Christoffel-Darboux formula for multiple orthogonal polynomials

The asymptotics of Hermite-Padé polynomials for two Markov-type functions

A problem is solved on the limit distribution of the zeros of polynomials which are simultaneously orthogonal on two intervals and of the real line such that , under the assumption that the ratio of

Random matrices with external source and the asymptotic behaviour of multiple orthogonal polynomials

Ensembles of random Hermitian matrices with a distribution measure defined by an anharmonic potential perturbed by an external source are considered. The limiting characteristics of the eigenvalue

Asymptotics of Hermite-Padé Polynomials

We review results about the asymptotic behavior (in the strong and weak sense) of Hermite-Pade polynomials of type II (also known as German polynomials). The polynomials appear as numerators and