Abstract:
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 discrete Nikishin system, and the other leads to essentially new effects. The limit distribution of the zeros of polynomials is obtained in terms of logarithmic equilibrium potentials and in terms of algebraic curves.
Bibliography: 9 titles.
This publication is cited in the following 27 articles:
W. Benamira, A. Nasri, “A d-orthogonal polynomial set of Meixner type”, Probl. anal. Issues Anal., 14:1 (2025), 22–41
A. I. Aptekarev, A. V. Dyachenko, V. G. Lysov, “Meixner Multiply Orthogonal Polynomials on Interleaved Lattices”, Math. Notes, 115:4 (2024), 642–646
R. M. Gadzhimirzaev, “Approximation properties of de la Vallée Poussin means of partial Fourier series in Meixner–Sobolev polynomials”, Sb. Math., 215:9 (2024), 1202–1223
V. G. Lysov, “Distribution of zeros of polynomials of multiple discrete orthogonality in the Angelesco case”, Russian Math. Surveys, 79:6 (2024), 1101–1103
V. N. Sorokin, “On Polynomials Defined by the Discrete Rodrigues Formula”, Math. Notes, 113:3 (2023), 420–433
V. N. Sorokin, “A generalization of the discrete Rodrigues formula for Meixner polynomials”, Sb. Math., 213:11 (2022), 1559–1581
V. N. Sorokin, “Recurrence Legendre polynomials”, Moscow University Mathematics Bulletin, 77:6 (2022), 255–261
Sorokin V.N., “Asymptotics of Hermite-Pade Approximants of the First Type For Discrete Meixner Measures”, Lobachevskii J. Math., 42:11, SI (2021), 2654–2667
V. N. Sorokin, “Hermite-Padé approximants to the Weyl function and its derivative for discrete measures”, Sb. Math., 211:10 (2020), 1486–1502
V. G. Lysov, D. N. Tulyakov, “On the supports of vector equilibrium measures in the Angelesco problem with nested intervals”, Proc. Steklov Inst. Math., 301 (2018), 180–196
V. N. Sorokin, “Multipoint Hermite–Padé approximants for three beta functions”, Trans. Moscow Math. Soc., 2018, 117–134
Alexander Viktorovich Dyachenko, Vladimir Genrikhovich Lysov, “On polynomials of multiple discrete orthogonality on lattices with shift”, KIAM Prepr., 2018, no. 218, 1
A. I. Aptekarev, G. López Lagomasino, A. Martínez-Finkelshtein, “On Nikishin systems with discrete components and weak asymptotics of multiple orthogonal polynomials”, Russian Math. Surveys, 72:3 (2017), 389–449
V. G. Lysov, D. N. Tulyakov, “On a Vector Potential-Theory Equilibrium Problem with the Angelesco Matrix”, Proc. Steklov Inst. Math., 298 (2017), 170–200
V. N. Sorokin, “On Multiple Orthogonal Polynomials for Three Meixner Measures”, Proc. Steklov Inst. Math., 298 (2017), 294–316
Driver K., Jooste A., “Interlacing of Zeros of Quasi-Orthogonal Meixner Polynomials”, Quaest. Math., 40:4 (2017), 477–490
V. N. Sorokin, “Angelesco–Meixner polynomials”, Keldysh Institute preprints, 2017, 27–16
V. N. Sorokin, “Ob asimptoticheskikh rezhimakh sovmestnykh mnogochlenov Meiksnera”, Preprinty IPM im. M. V. Keldysha, 2016, 046, 32 pp.
V. G. Lysov, D. N. Tulyakov, “O vektornoi teoretiko-potentsialnoi zadache s matritsei Anzhelesko”, Preprinty IPM im. M. V. Keldysha, 2016, 110, 36 pp.
V. N. Sorokin, “Simultaneous orthogonal polynomials related to Poisson distribution”, Moscow University Mathematics Bulletin, 70:1 (2015), 1–5
Citation in format AMSBIB
Contact us: