We discuss the essential self-adjointness of wave operators, as well as the limiting absorption principle, in generalizations of asymptotically Minkowski settings. This is obtained via using a Fredholm framework for inverting the spectral family first, and then refining its conclusions to show dense range of − λ, λ / ∈ R, in Lsc when acting on an appropriate subdomain.

We characterize abstract Morita contexts in several bicategories. In particular, we use heteromorphisms for the bicategory Prof of categories and profunctors and coreflective subcategories for Cat (categories and functors). In addition, we prove general statements concerning strict Morita contexts, and we give new equivalent forms to the standard notions of adjointness, category equivalence and...

In this paper, projective modules over a quantale are characterized by distributivity, continuity, and adjointness conditions. It is then show that a morphism Q // A of commutative quantales is coexponentiable if and only if the corresponding Q-module is projective, and hence, satisfies these equivalent conditions.

We examine the detail of the analytic structure of an exact analytic solution of three anyons, which interpolates to the fermion ground state in a harmonic potential well. The analysis is done on the fundamental domain with appropriate boundary conditions. Some remarks on the hard-core conditions and self-adjointness are made.

In this paper, we consider an impulsive Sturm-Lioville problem on Sturmian time scales. We investigate the existence and uniqueness of solution problem. study some spectral properties self-adjointness boundary-value Later, construct Green function for Finally, eigenfunction expansion is obtained.

A general formalism is presented for the solution of boundary value problems arising in the description of transport of mass or energy through multiphase media, which consists in identifying physical conditions of interfaces with criteria for self-adjointness of the operators concerned. Several examples have been presented which demonstrate the advantages of the formalism.

we investigate the boundary-value problem generated by the sturm-liouville equation withdiscontinuous coefficients, eigenparameter dependent boundary conditions and transmission conditionsat the point of discontinuity. with a different approach we introduce an adequate hilbert spaceformulation, investigate some properties of eigenvalues, green’s function and resolvent operator, andfind simple c...

‘One universe, one logic’ takes the world as it is and leads to adjointness as the global logic of anything. The alternative approach to find a unification of known logics requires assumptions and is therefore consistent with the same conclusion for a universal logic has to be universally applicable. The universal characteristic of adjointness is that it has a natural construction from the conc...

The purpose of this note is to present several criteria for essential self– adjointness. The method is based on ideas due to Shubin. This note is divided into two parts. The first part deals with symmetric first order systems on the line in the most general setting. Such a symmetric first order system of differential equations gives rise naturally to a symmetric linear relation in a Hilbert spa...

We study dynamics of a scalar field in the near-horizon region described by a static Klein-Gordon operator which is the Hamiltonian of the system. The explicite construction of a time operator near-horizon is given and its self-adjointness discussed. ⋆ Expanded version of a poster presented at the 5 European Advanced Study Conference in Ancient Olympia, Greece, May 2004. Preprint submitted to E...