106 citations · 454 across the 52 of their papers we have counts for
55 papers
Sharp Hardy's Inequalities in Hilbert Spaces
Dimitar K. Dimitrov, Ivan Gadjev, Mourad E. H. Ismail
We study the behavior of the smallest possible constants and in Hardy's inequalities $$ \int_a^b\left(\frac{1}{x}\int_a^xf(t)dt\right)^2\,dx\leq d(a,b)\,\int_a^b [f(…
Orthogonal Polynomials of Askey-Wilson Type
Mourad E. H. Ismail, Ruiming Zhang, Keru Zhou
We study two families of orthogonal polynomials. The first is a finite family related to the Askey-Wilson polynomials but the orthogonality is on the real line. A limiting case of…
-type Lidstone expansions and an interpolation problem for entire functions
Mourad E. H. Ismail, Zeinab S. I. Mansour
In this paper, we expand functions of specific -exponential growth in terms of its even (odd) Askey- Wilson -derivatives at and . This expansion i…
q-Fractional Askey-Wilson Integrals and Related Semigroups of Operators
Mourad E. H. Ismail, Ruiming Zhang, Keru Zhou
We introduce three one-parameter semigroups of operators and determine their spectra. Two of them are fractional integrals associated with the Askey-Wilson operator. We also study…
The Asymptotic Iteration Method Revisited
Mourad E. H. Ismail, Nasser Saad
The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems th…
A discrete and Asymptotic Iteration Method
Mourad E. H. Ismail, Nasser Saad
We introduce a finite difference and -difference analogues of the Asymptotic Iteration Method of Ciftci, Hall, and Saad. We give necessary, and sufficient condition for the exis…