Entropy of Hermite polynomials with application to the harmonic oscillator.
Error bounds of some Gauss-turan-kronrod quadratures with Gori-micchelli weights for analytic functions
Estimates for polynomials orthogonal with respect to some Gegenbauer-Sobolev type inner product.
Exact solutions of the semi-infinite Toda lattice with applications to the inverse spectral problem.
Exponential Riordan arrays and permutation enumeration.
Fejér–Riesz factorizations and the structure of bivariate polynomials orthogonal on the bi-circle
We give a complete characterization of the positive trigonometric polynomials on the bi-circle, which can be factored as where is a polynomial nonzero for and . The conditions are in terms of recurrence coefficients associated with the polynomials in lexicographical and reverse lexicographical ordering orthogonal with respect to the weight on the bi-circle. We use this result to describe how specific factorizations of weights on the bi-circle can be translated into identities relating...
Fine structure of the zeros of orthogonal polynomials. I: A tale of two pictures.
Fourier-Bessel functions of singular continuous measures and their many asymptotics.
Gaussian quadrature for matrix valued functions on the unit circle.
Generalisations of some properties of invariant polynomials with matrix arguments
Some extensions of the properties of invariant polynomials proved by Davis (1980), Chikuse (1980), Chikuse and Davis (1986) and Ratnarajah et al. (2005) are given for symmetric and Hermitian matrices.
Generalized Rudin-Shapiro Systems.
Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials: a survey.
Generating new classes of orthogonal polynomials.
Generating some semiclassical orthogonal polynomials.
Geometric Fourier analysis
In this paper we continue the study of the Fourier transform on , , analyzing the “almost-orthogonality” of the different directions of the space with respect to the Fourier transform. We prove two theorems: the first is related to an angular Littlewood-Paley square function, and we obtain estimates in terms of powers of , where is the number of equal angles considered in . The second is an extension of the Hardy-Littlewood maximal function when one consider cylinders of , , of fixed eccentricity...
Global orthogonality implies local almost-orthogonality.
We introduce a new stopping-time argument, adapted to handle linear sums of noncompactly-supported functions that satisfy fairly weak decay, smoothness, and cancellation conditions. We use the argument to obtain a new Littlewood-Paley-type result for such sums.
Integrability behaviour of the maximal partial sum of orthogonal series.
Integral representations for multiple Hermite and multiple Laguerre polynomials
We give integral representations for multiple Hermite and multiple Laguerre polynomials of both type I and II. We also show how these are connected with double integral representations of certain kernels from random matrix theory.
Jacobi matrices on trees
Symmetric Jacobi matrices on one sided homogeneous trees are studied. Essential selfadjointness of these matrices turns out to depend on the structure of the tree. If a tree has one end and infinitely many origin points the matrix is always essentially selfadjoint independently of the growth of its coefficients. In case a tree has one origin and infinitely many ends, the essential selfadjointness is equivalent to that of an ordinary Jacobi matrix obtained by restriction to the so called radial functions....
Jacobi-Sobolev orthogonal polynomials: asymptotics for -coherence of measures.