Support of the extremal measure in a vector equilibrium problem

Lapik, M A

doi:10.1070/sm2006v197n08abeh003795

Cited by 9 publications

(11 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…As it was pointed out by one of the referees, examples of of algebraic curves for special external fields were also obtained in the recent papers [11,12].…”

Section: Introductionmentioning

confidence: 89%

“…Ψ ) vanishing at the endpoints of the supports for the measures of the corresponding Nikishin problem. Along similar lines, examples of curves of algebraic type for Nikishin systems with special choices of external fields were recently obtained in[11].…”

mentioning

confidence: 91%

“…The original problem was introduced in [8] (without external fields) and further questions have been addressed in [9,16,10,1,11]. The main motivation of our interest for this problem arises in a recently introduced set of biorthogonal polynomials [2].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Regularity of a vector potential problem and its spectral curve

Balogh

Bertola

2009

Journal of Approximation Theory

View full text Add to dashboard Cite

In this note we study a minimization problem for a vector of measures subject to a prescribed interaction matrix in the presence of external potentials. The conductors are allowed to have zero distance from each other but the external potentials satisfy a growth condition near the common points.We then specialize the setting to a specific problem on the real line which arises in the study of certain biorthogonal polynomials (studied elsewhere) and we prove that the equilibrium measures solve a pseudoalgebraic curve under the assumption that the potentials are real analytic. In particular, the supports of the equilibrium measures are shown to consist of a finite union of compact intervals.

show abstract

“…As it was pointed out by one of the referees, examples of of algebraic curves for special external fields were also obtained in the recent papers [11,12].…”

Section: Introductionmentioning

confidence: 89%

mentioning

confidence: 91%

See 1 more Smart Citation

Regularity of a vector potential problem and its spectral curve

Balogh

Bertola

2009

Journal of Approximation Theory

View full text Add to dashboard Cite

show abstract

“…To this end, we mention [25] for the study of weak asymptotics of generalized Pollaczek polynomials and [24] for the study of logarithmic asymptotics of multiple orthogonal polynomials with respect to weights with bounded support without considering the recurrence relation. We also refer the reader to [18] for an investigation of supports of the extreme measure in a vector equilibrium problem and to [13,15] for recent applications of vector equilibrium problems in some random models.…”

Section: )mentioning

confidence: 99%

The asymptotic zero distribution of multiple orthogonal polynomials associated with Macdonald functions

Zhang

Román

2011

Journal of Approximation Theory

View full text Add to dashboard Cite

We study the asymptotic zero distribution of type II multiple orthogonal polynomials associated with two Macdonald functions (modified Bessel functions of the second kind). On the basis of the four-term recurrence relation, it is shown that, after proper scaling, the sequence of normalized zero counting measures converges weakly to the first component of a vector of two measures which satisfies a vector equilibrium problem with two external fields. We also give the explicit formula for the equilibrium vector in terms of solutions of an algebraic equation.

show abstract

“…Рассматриваемая вариационная задача по сути такая же, как за-дачи, возникающие в теории аппроксимаций Эрмита-Паде (см. [15], [18]- [22]). В процессе проверки решения вариационной задачи также доказана ее эквива-лентность (в рассматриваемом случае) некоторой другой вариационной задаче с ограничением на величины мер.…”

Section: )unclassified