In this paper we consider a second order, Sturm-Liouville-type boundary-value operator of the form Lu := −[pu∇]∆ + qu, on an arbitrary, bounded time-scale T, for suitable functions p, q, together with suitable boundary conditions. We show that, with a suitable choice of domain, this operator can be formulated in the Hilbert space L(Tκ), in such a way that the resulting operator is self-adjoint,...

Many different proposals exist for the definition of lower and upper approximation operators in covering-based rough sets. In this paper, we establish relationships between the most commonly used operators, using especially concepts of duality, conjugacy and adjointness (also referred to as Galois connection). We highlight the importance of the adjointness condition as a way to provide a meanin...

This note adds three annexes to my previous paper math/9904044 Annex 1. A sufficient condition for self-adjointness Annex 2. Invariant closed operators on locally compact abelian groups Annex 3. The trace of Connes for quaternions This last item is a minor variation on the evaluation of Connes’s trace (math/9811068), which is explained here in the setting of quaternions and can be applied also ...

We prove a new criterion that guarantees self-adjointness of Toeplitz operators with unbounded operator-valued symbols. Our applies, in particular, to symbols Lipschitz continuous derivatives, which is the natural class Hamiltonian functions for classical mechanics. For this we extend Berger-Coburn estimate case vector-valued Segal-Bargmann spaces. Finally, apply our result (operator-valued) qu...

In this paper we consider linear ordinary elliptic differential operators with smooth coefficients on finite quantum graphs. We discuss criteria for the operator to be self-adjoint. This involves conditions on matrices representative of the boundary conditions at each vertex. The main point is the development of a Maple application to test these conditions.

In this article, linear operators satisfying anti-commutation relations are considered. It is proven that an anti-commutative type of the Glimm-Jaffe-Nelson commutator theorem follows.