Scattering theory and polynomials orthogonal on the unit circle
From MaRDI portal
Publication:3881130
DOI10.1063/1.524077zbMath0439.33014OpenAlexW2036305183MaRDI QIDQ3881130
K. M. Case, Jeffrey S. Geronimo
Publication date: 1979
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.524077
scattering theorypolynomials orthogonal on the unit circleJost functionSzegö's theorem on Toeplitz determinants
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Scattering theory of linear operators (47A40) Other special functions (33E99)
Related Items
Géza Freud, orthogonal polynomials and Christoffel functions. A case study, Fredholm Determinant Evaluations of the Ising Model Diagonal Correlations and their λ Generalization, A Riemann-Hilbert approach to some theorems on Toeplitz operators and orthogonal polynomials, On extensions of a theorem of Baxter, Patterns and structure in systems governed by linear second-order differential equations, Subcritical multiplicative chaos for regularized counting statistics from random matrix theory, Scattering Theory and Polynomials Orthogonal on the Real Line, Asymptotics of block Toeplitz determinants and the classical dimer model, Harold Widom’s work in random matrix theory, Harold Widom’s work in Toeplitz operators, Meromorphic Szegő functions and asymptotic series for Verblunsky coefficients, A Relation between the Coefficients in the Recurrence Formula and the Spectral Function for Orthogonal Polynomials, Szegő via Jacobi, Toeplitz Matrices and Toeplitz Determinants under the Impetus of the Ising Model: Some History and Some Recent Results, Periodic TASEP with general initial conditions, Exact solution of the classical dimer model on a triangular lattice: monomer-monomer correlations, \(m\)-functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices, Long-time large-distance asymptotics of the transverse correlation functions of the XX chain in the spacelike regime, Modulated bi-orthogonal polynomials on the unit circle: the \(2j-k\) and \(j-2k\) systems, Integrable equations associated with the finite‐temperature deformation of the discrete Bessel point process, From Berry-Esseen to super-exponential, Complex eigenvalue instantons and the Fredholm determinant expansion in the Gross-Witten-Wadia model, Harold Widom's contributions to the spectral theory and asymptotics of Toeplitz operators and matrices, Non-colliding Brownian motions and the extended tacnode process, Szegő's theorem and its probabilistic descendants, The Hilbert series of \(\mathcal{N}=1\) \(SO(N_c)\) and \(Sp(N_c)\) SQCD, Painlevé VI and integrable systems, Borodin-Okounkov and Szegő for Toeplitz operators on model spaces, The Hilbert series of U/SU SQCD and Toeplitz determinants, Block Toeplitz determinants, constrained KP and Gelfand-Dickey hierarchies, Meromorphic Jost functions and asymptotic expansions for Jacobi parameters, Powers of large random unitary matrices and Toeplitz determinants, Limit theorems for biorthogonal ensembles and related combinatorial identities, On the diagonal susceptibility of the two-dimensional Ising model, Higher order asymptotics of Toeplitz determinants with symbols in weighted Wiener algebras, Painlevé formulas of the limiting distributions for nonnull complex sample covariance matrices, Crossing bridges with strong Szegő limit theorem, Spectrum, asymptotic invertibility and Szegö type theorems of Dirichlet Toeplitz operators, High-temperature analysis of the transverse dynamical two-point correlation function of the XX quantum-spin chain, Multivariate normal approximation for traces of random unitary matrices, Scattering theory and matrix orthogonal polynomials on the real line, Orthogonal Polynomials, Measures and Recurrences on the Unit Circle, Matrix orthogonal polynomials on the unit circle, Traces of Commutators of Integral Operators – the Aftermath, Some remarks on the generalized Gelfand-Levitan equation, New results for the SQCD Hilbert series, Matrix models and stochastic growth in Donaldson-Thomas theory, Universality of mesoscopic fluctuations for orthogonal polynomial ensembles
Cites Work
- Fredholm determinants and inverse scattering problems
- Asymptotic behavior of block Toeplitz matrices and determinants. II
- On a theorem of Szegö, Kac, and Baxter
- Asymptotic behavior of Toeplitz matrices and determinants
- Polynomials defined by a difference system
- Toeplitz matrices, translation kernels and a related problem in probability theory
- Nonlinear differential−difference equations
- Fredholm determinants and multiple solitons
- Orthogonal polynomials from the viewpoint of scattering theory