Results 41 to 50 of about 1,174 (70)
Surveys in Approximation Theory, 1 (2005), 70-125, 2005 In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.
arxiv
Lowering and raising operators for the free Meixner class of orthogonal polynomials [PDF]
arXiv, 2008 We compare some properties of the lowering and raising operators for the classical and free classes of Meixner polynomials on the real line.
arxiv
Orthogonal polynomials for the weight $x^ν \exp(-x - t/x)$ [PDF]
arXiv, 2021 Orthogonal polynomials for the weight $x^{\nu} \exp(-x - t/x),\ x, t > 0, \nu \in \mathbb{R}$ are investigated. Differential-difference equations, recurrence relations, explicit representations, generating functions and Rodrigues-type formula are obtained.
arxiv
Generalized Catalan recurrences, Riordan arrays, elliptic curves, and orthogonal polynomials [PDF]
arXiv, 2019 We show that the Catalan-Schroeder convolution recurrences and their higher order generalizations can be solved using Riordan arrays and the Catalan numbers. We investigate the Hankel transforms of many of the recurrence solutions, and indicate that Somos $4$ sequences often arise.
arxiv
Divergent Cesaro and Riesz means of Jacobi and Laguerre expansions [PDF]
arXiv, 2002 We show that for $\delta$ below certain critical indices there are functions whose Jacobi or Laguerre expansions have almost everywhere divergent Cesaro and Riesz means of order $\delta$.
arxiv
An inequality on Chebyshev polynomials [PDF]
arXiv, 2003 We define a class of multivariate Laurent polynomials closely related to Chebyshev polynomials, and prove the simple but somewhat surprising (in view of the fact that the signs of the coefficients of the Chebyshev polynomials themselves alternate) result that their coefficients are non-negative.
arxiv
A note on circular trace formulae [PDF]
arXiv, 2006 We find a finite CMV matrix whose eigenvalues coincide with the Dirichlet data of a circular periodic problem. As a consequence, we obtain circular analogues of the classical trace formulae for periodic Jacobi matrices.
arxiv
Almost Periodic Szegő Cocycles with Uniformly Positive Lyapunov Exponents [PDF]
J. Approx. Theory 161 (2009), 813-818, 2008 We exhibit examples of almost periodic Verblunsky coefficients for which Herman's subharmonicity argument applies and yields that the associated Lyapunov exponents are uniformly bounded away from zero.
arxiv
Spectra of Self-Similar Measures. [PDF]
Entropy (Basel), 2022 Cao YS, Deng QR, Li MT.
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Area Littlewood-Paley functions associated with Hermite and Laguerre operators [PDF]
arXiv, 2010 In this paper we study Lp-boundedness properties for area Littlewood-Paley functions associated with heat semigroups for Hermite and Laguerre ...
arxiv