Polinomios ortogonales sobre la circunferencia unidad. Los casos C y D.
Polynomial approximation and twenty years later.
Polynomial sequences generated by infinite Hessenberg matrices
We show that an infinite lower Hessenberg matrix generates polynomial sequences that correspond to the rows of infinite lower triangular invertible matrices. Orthogonal polynomial sequences are obtained when the Hessenberg matrix is tridiagonal. We study properties of the polynomial sequences and their corresponding matrices which are related to recurrence relations, companion matrices, matrix similarity, construction algorithms, and generating functions. When the Hessenberg matrix is also Toeplitz...
Positivity of Cotes Numbers at More Jacobi Abscissas.
Pseudo-orthogonal polynomials.
Quadrature formulas for rational functions.
Quasi-definiteness of generalized Uvarov transforms of moment functionals.
Quasi-orthogonality on the unit circle and semi-classical forms.
Recent trends on analytic properties of matrix orthonormal polynomials.
Recurrence relations for orthogonal polynomials on algebraic curves
Recurrence relations with periodic coefficients and Chebyshev polynomials
We show that polynomials defined by recurrence relations with periodic coefficients may be represented with the help of Chebyshev polynomials of the second kind.
Remark on the inequality of F. Riesz
We prove F. Riesz’ inequality assuming the boundedness of the norm of the first arithmetic mean of the functions with p ≥ 2 instead of boundedness of the functions φₙ of an orthonormal system.
Remarks on orthogonal polynomials with respect to varying measures and related problems.
Restricted permutations and Chebyshev polynomials.
Restricted permutations, continued fractions, and Chebyshev polynomials.
Riordan arrays, orthogonal polynomials as moments, and Hankel transforms.
Rodrigues-type formulae for Hermite and Laguerre polynomials.
Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model.
Sharp estimates of the Jacobi heat kernel
The heat kernel associated with the setting of the classical Jacobi polynomials is defined by an oscillatory sum which cannot be computed explicitly, in contrast to the situation for the other two classical systems of orthogonal polynomials. We deduce sharp estimates giving the order of magnitude of this kernel, for type parameters α, β ≥ -1/2. Using quite different methods, Coulhon, Kerkyacharian and Petrushev recently also obtained such estimates. As an application of the bounds, we show that...
Skew-orthogonal polynomials of a discrete variable.