22 research outputs found
On sampling theory and basic SturmâLiouville systems
AbstractWe investigate the sampling theory associated with basic SturmâLiouville eigenvalue problems. We derive two sampling theorems for integral transforms whose kernels are basic functions and the integral is of Jackson's type. The kernel in the first theorem is a solution of a basic difference equation and in the second one it is expressed in terms of basic Green's function of the basic SturmâLiouville systems. Examples involving basic sine and cosine transforms are given
The roots of the third Jackson q-Bessel function
We derive analytic bounds on the roots of the third Jackson Function.
This bounds prove a conjecture of M. E. H. Ismail concerning
the asymptotic behaviour of the roots
Determinant inequalities for sieved ultraspherical polynomials
Paul Turan first observed that the Legendre polynomials satisfy
the inequality Pn2(x)âPnâ1(x)Pn(x)>0, â1<x<1. Inequalities of this type have since been proved for both
classical and nonclassical orthogonal polynomials. In this
paper, we prove such an inequality for sieved orthogonal
polynomials of the second kind
On Sampling Theory And Basic Sturm-Liouville Systems
We investigate the sampling theory associated with basic Sturm-Liouville eigenvalue problems. We derive two sampling theorems for integral transforms whose kernels are basic functions and the integral is of Jackson\u27s type. The kernel in the first theorem is a solution of a basic difference equation and in the second one it is expressed in terms of basic Green\u27s function of the basic Sturm-Liouville systems. Examples involving basic sine and cosine transforms are given. © 2006 Elsevier B.V. All rights reserved
© Hindawi Publishing Corp. THE ROOTS OF THE THIRD JACKSON q-BESSEL FUNCTION
We derive analytic bounds for the zeros of the third Jackson q-Bessel functio