We study here the action of subgroups of PSL(2, R) on the space of harmonic functions on the unit disc bounded by a common constant, as well as the relationship this action has with the foliated Liouville problem: Given a foliation of a compact manifold by Riemannian leaves and a leafwise harmonic continuous function on the manifold, is the function leafwise constant? We give a number of positi...

A symplectic theory approach is devised for solving the problem of algebraic-analytical construction of integral submanifold imbeddings for integrable (via the nonabelian Liouville-Arnold theorem) Hamiltonian systems on canonically symplectic phase spaces.

In this paper we investigate a Sturm–Liouville eigenvalue problem on time scales. Existence of the eigenvalues and eigenfunctions is proved. Mean square convergent and uniformly convergent expansions in the eigenfunctions are established. AMS subject classification: 34L10.