We establish Hardy-type inequalities for the Riemann-Liouville and Weyl transforms associated with the Jacobi operator by using Hardy-type inequalities for a class of integral operators.

This paper considers the problem of viscous dissipation in the flow of Newtonian fluid through a tube of annular cross section, with Dirichlet boundary conditions. The solution of the problem is obtained by a series expansion about the complete eigenfunctions system of a Sturm-Liouville problem. Eigenfunctions and eigenvalues of this Sturm-Liouville problem are obtained by Galerkin’s method.

The classical field equations of a Liouville field coupled to gravity in two spacetime dimensions are shown to have black hole solutions. Exact solutions are also obtained when quantum corrections due to back reaction effects are included, modifying both the ADM mass and the black hole entropy. The thermodynamic limit breaks down before evaporation of the black hole is complete, indicating that...

We derive Povzner–Wienholtz-type self-adjointness results form× m matrix-valued Sturm–Liouville operators T = R [