Search Results - "Aptekarev, A. I."

Weak and Strong Asymptotics of Orthogonal Polynomials with Varying Weight by Aptekarev, A. I.

“…We consider sequences of orthogonal polynomials with varying weights, i.e., depending on the number of the polynomial. We obtain extensions of applicability…”
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Multiple orthogonal polynomials for classical weights by Aptekarev, A. I., Branquinho, A., Van Assche, W.

“…A new set of special functions, which has a wide range of applications from number theory to integrability of nonlinear dynamical systems, is described. We…”
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Multiple orthogonal polynomials by Aptekarev, A.I.

“…Results on multiple orthogonal polynomials will be surveyed. Multiple orthogonal polynomials are intimately related to Hermite-Padé approximants and often they…”
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Meixner Multiple Orthogonal Polynomials on Interlacing Lattices by Aptekarev, A. I., Dyachenko, A. V., Lysov, V. G.

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Emergence of a Hierarchy of Singularities in Zero-Pressure Media. Two-Dimensional Case by Aptekarev, A. I., Rykov, Yu. G.

“…Generalized solutions of the system of zero-pressure gas dynamics equations in the case of two spatial variables are considered. In contrast to the…”
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Volume Conjecture and WKB Asymptotics by Aptekarev, A. I., Dudnikova, T. V., Tulyakov, D. N.

“…We consider -difference equations for colored Jones polynomials. These polynomials are invariants for the knots and their asymptotics plays an important role…”
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Recurrence Relations and Asymptotics of Colored Jones Polynomials by Aptekarev, A. I., Dudnikova, T. V., Tulyakov, D. N.

“…We consider -difference equations for colored Jones polynomials. These sequences of polynomials are invariants for the knots and their asymptotics plays an…”
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About the Works of K. I. Babenko in the Field of Mechanics and Applied Mathematics (on the 100th Anniversary of His Birth) by Aptekarev, A. I., Afendikova, N. G.

“…The paper provides an overview of the scientific achievements of K.I. Babenko, Corresponding Member of Academy of Sciences of the USSR, in the field of…”
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Detailed Description of the Evolution Mechanism for Singularities in the System of Pressureless Gas Dynamics by Aptekarev, A. I., Rykov, Yu. G.

“…The system of pressureless gas dynamics is a hydrodynamically justified generalization of the system consisting of the Burgers vector equation in the limit of…”
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Discrete Schrödinger Operator on a Tree, Angelesco Potentials, and Their Perturbations by Aptekarev, A. I., Denisov, S. A., Yattselev, M. L.

“…We consider a class of discrete Schrödinger operators on an infinite homogeneous rooted tree. Potentials for these operators are given by the coefficients of…”
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Hesse Parametrization of a Spectral Curve by Aptekarev, A. I., Tulyakov, D. N.

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Direct and inverse problems for vector logarithmic potentials with external fields by Aptekarev, A. I., Lapik, M. A., Lysov, V. G.

“…We consider extremal problems for the energy of the logarithmic potential with external fields closely related with the inverse spectral problem method. The…”
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Asymptotics of orthogonal polynomial’s entropy by Aptekarev, A.I., Dehesa, J.S., Martinez-Finkelshtein, A.

“…This is a brief account on some results and methods of the asymptotic theory dealing with the entropy of orthogonal polynomials for large degree. This study is…”
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On Asymptotics of the Sharp Constants of the Markov–Bernshtein Inequalities for the Sobolev Spaces by Aptekarev, A. I., Draux, A., Tulyakov, D. N.

“…The Sobolev spaces with continuous and discrete coherent pairs of weights are considered. The positivity of the inner product is equivalent to the…”
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Asymptotics of sharp constants of Markov-Bernstein inequalities in integral norm with Jacobi weight by APTEKAREV, A. I., DRAUX, A., KALYAGIN, V. A., TULYAKOV, D. N.

“…The classical A. Markov inequality establishes a relation between the maximum modulus or the L^{\infty }\left ([-1,1]\right ) norm of a polynomial Q_{n} and of…”
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Asymptotic behavior of the spectrum of combination scattering at Stokes phonons by Aptekarev, A. I., Lapik, M. A., Orlov, Yu. N.

“…For a class of polynomial quantum Hamiltonians used in models of combination scattering in quantum optics, we obtain the asymptotic behavior of the spectrum…”
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Toda-type differential equations for the recurrence coefficients of orthogonal polynomials and Freud transformation by Aptekarev, A.I., Branquinho, A., Marcellán, F.

“…Transformations of the measure of orthogonality for orthogonal polynomials, namely Freud transformations, are considered. Jacobi matrix of the recurrence…”
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Hyperelliptic uniformization of algebraic curves of the third order by Aptekarev, A.I., Toulyakov, D.N., Van Assche, W.

“…An algebraic function of the third order plays an important role in the problem of asymptotics of Hermite–Padé approximants for two analytic functions with…”
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Equilibrium of vector potentials and uniformization of the algebraic curves of genus 0 by Aptekarev, A.I., Kalyagin, V.A., Lysov, V.G., Toulyakov, D.N.

“…We consider equilibrium problems for the logarithmic vector potential related to the asymptotics of the Hermite–Padé approximants. Solutions of such problems…”
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Scalar and matrix Riemann–Hilbert approach to the strong asymptotics of Padé approximants and complex orthogonal polynomials with varying weight by Aptekarev, A.I, Van Assche, W

“…We describe methods for the derivation of strong asymptotics for the denominator polynomials and the remainder of Padé approximants for a Markov function with…”
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