We establish an integral representation of a right inverse of the Askey-Wilson finite difference operator on L2 with weight (1−x2)−1/2. The kernel of this integral operator is θ′4/θ4 and is the Riemann mapping function that maps the open unit disc conformally onto the interior of an ellipse. Running title: An Inverse Operator 1990 Mathematics Subject Classification: Primary 33D45, 42C10, Second...

This chapter illustrates the use of Gabor frame analysis to derive results on the spectral properties of integral and pseudodifferential operators. In particular, we obtain a sufficient condition on the kernel of an integral operator or the symbol of a pseudodifferential operator which implies that the operator is trace-class. This result significantly improves a sufficient condition due to Dau...

This paper presents a posteriori error estimates for the hp{version of the boundary element method. We discuss two rst kind integral operator equations, namely Symm's integral equation and the integral equation with a hypersingular operator. The computable upper error bounds indicate an algorithm for the automatic hp{adaptive mesh{reenement. The eeciency of this method is shown by numerical exp...

This paper presents a posteriori error estimates for the hp{version of the boundary element method. We discuss two rst kind integral operator equations , namely Symm's integral equation and the integral equation with a hypersingular operator. The computable upper error bounds indicate an algorithm for the automatic hp{adaptive mesh{reenement. The eeciency of this method is shown by numerical ex...

‎Some functional inequalities‎ ‎in variable exponent Lebesgue spaces are presented‎. ‎The bi-weighted modular inequality with variable exponent $p(.)$ for the Hardy operator restricted to non‎- ‎increasing function which is‎‎$$‎‎int_0^infty (frac{1}{x}int_0^x f(t)dt)^{p(x)}v(x)dxleq‎‎Cint_0^infty f(x)^{p(x)}u(x)dx‎,‎$$‎ ‎is studied‎. ‎We show that the exponent $p(.)$ for which these modular ine...

In this paper, we investigate some properties for an integral operator defined by Al-Oboudi differential operator.