Recent advances in asymptotic analysis

DOI10.1142/S0219530522400012zbMath1501.41009arXiv2204.09305MaRDI QIDQ5049156

Yu-Qiu Zhao, Roderick Wong

Publication date: 11 November 2022

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.09305

zbMATH Keywords

asymptoticsparametrixuniform asymptotic expansionsRiemann-Hilbert approachWiener-Hopf equationssecond-order difference equationsDarboux's method

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Linear integral equations (45A05) Linear difference equations (39A06)

Related Items

Symbolic computation of recurrence coefficients for polynomials orthogonal with respect to the Szegő-Bernstein weights

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Critical edge behavior and the Bessel to Airy transition in the singularly perturbed Laguerre unitary ensemble
• Plancherel-Rotach asymptotic expansion for some polynomials from indeterminate moment problems
• Equations of Wiener-Hopf type
• Uniform asymptotics of orthogonal polynomials arising from coherent states
• Asymptotics of orthogonal polynomials via the Riemann-Hilbert approach
• Resurrecting the asymptotics of linear recurrences
• Quadrature formulas for oscillatory integral transforms
• Asymptotic expansions for second-order linear difference equations
• The isomonodromy approach to matrix models in 2D quantum gravity
• The early history of the factorial function
• Some indetermining moment problems and Freud-like weights
• Level-spacing distributions and the Airy kernel
• Level spacing distributions and the Bessel kernel
• Asymptotic expansions for second-order linear difference equations with a turning point
• Uniform asymptotic expansion of \(J_\nu(\nu a)\) via a difference equation
• Asymptotics of polynomials orthogonal with respect to a logarithmic weight
• On a uniform treatment of Darboux's method
• Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model
• Analytic theory of singular difference equations
• The Riemann--Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]
• The spectrum edge of random matrix ensembles.
• Gap probability of the circular unitary ensemble with a Fisher-Hartwig singularity and the coupled Painlevé V system
• The method of Darboux
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• A uniform asymptotic expansion for Jacobi polynomials via uniform treatment of Darboux's method
• The asymptotic evaluation of certain integrals
• A uniform treatment of Darboux's method
• Special functions, integral equations and a Riemann-Hilbert problem
• Uniform treatment of Darboux’s method and the Heisenberg polynomials
• Complex Gaussian quadrature for oscillatory integral transforms
• LINEAR DIFFERENCE EQUATIONS WITH A TRANSITION POINT AT THE ORIGIN
• Exact Remainders for Asymptotic Expansions of Fractional Integrals
• Sound transmission from a tube with flow
• Systems of integral equations on a half line with kernels depending on the difference of arguments
• Generalized Mellin Convolutions and their Asymptotic Expansions
• Discrete Orthogonal Polynomials. (AM-164): Asymptotics and Applications (AM-164)
• Uniform asymptotics for orthogonal polynomials via the Riemann--Hilbert approach
• Asymptotic Expansions for Second-Order Linear Difference Equations, II
• Explicit Error Terms for Asymptotic Expansions of Stieltjes Transforms
• Uniform Airy-Type Expansions of Integrals
• Error Bounds for Asymptotic Expansions of Laplace Convolutions
• On the Asymptotic Solutions of Ordinary Differential Equations, With an Application to the Bessel Functions of Large Order
• Linear difference equations with transition points
• Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
• Asymptotic Solutions of Linear Volterra Integral Equations With Singular Kernels
• Rigorous WKB for Finite-Order Linear Recurrence Relations with Smooth Coefficients
• Asymptotic Behavior of the Pollaczek Polynomials and Their Zeros
• Asymptotic expansions for Wiener–Hopf equations
• Explorations in Complex Functions
• Asymptotics of linear recurrences
• Asymptotics of the Wilson polynomials
• Bessel-type asymptotic expansions via the Riemann–Hilbert approach
• WKB methods for difference equations I
• A Paradox in Asymptotics
• Note on an asymptotic property of solutions to a class of Fredholm integral equations
• Integral equations on a half-line with kernel depending upon the difference of the arguments
• Asymptotic Solutions of Certain Ordinary Differential Equations Associated with Multiple Roots of the Characteristic Equation
• The reflection of an electromagnetic plane wave by an infinite set of plates. I
• The Asymptotic Solutions of Ordinary Linear Differential Equations of the Second Order, With Special Reference to a Turning Point
• Uniform Asymptotic Expansions
• A New Absolute Geometric Constant?
• Discrete orthogonal polynomial ensembles and the Plancherel measure
• A Riemann-Hilbert approach to asymptotic questions for orthogonal polynomials
• Asymptotic behavior and zero distribution of polynomials orthogonal with respect to Bessel functions