Inequalities for orthonormal Laguerre polynomials

On orthonormal Muntz-Laguerre filters

Recently an upsurge in research relating to Laguerre filters for use in system optimization [1], system identification [2] and reduced-order modeling [3] has been noticed. The main reason for the good performance of Laguerre filters is that they form a uniformly bounded orthonormal basis in Hardy space [1]. Another reason, and this represents the novelty of the work carried out in this paper, i...

Jensen Polynomials and the Turan and Laguerre Inequalities

Laguerre and Jacobi polynomials

We present results on co-recursive associated Laguerre and Jacobi polynomials which are of interest for the solution of the Chapman-Kolmogorov equations of some birth and death processes with or without absorption. Explicit forms, generating functions, and absolutely continuous part of the spectral measures are given. We derive fourth-order differential equations satisfied by the polynomials wi...

Laguerre-type Bell polynomials

We develop an extension of the classical Bell polynomials introducing the Laguerre-type version of this well-known mathematical tool. The Laguerre-type Bell polynomials are useful in order to compute the nth Laguerre-type derivatives of a composite function. Incidentally, we generalize a result considered by L. Carlitz in order to obtain explicit relationships between Bessel functions and gener...

Jacobi Polynomials, Bernstein-type Inequalities and Dispersion Estimates for the Discrete Laguerre Operator

The present paper is about Bernstein-type estimates for Jacobi polynomials and their applications to various branches in mathematics. This is an old topic but we want to add a new wrinkle by establishing some intriguing connections with dispersive estimates for a certain class of Schrödinger equations whose Hamiltonian is given by the generalized Laguerre operator. More precisely, we show that ...