We consider the question: To what extend does the Weyl function (i.e., the abstract Dirichlet-to-Neumann map) see the same singularities as the resolvent of some restriction of the maximal operator. The proper, so-called detectable, subspace will be introduced and analyzed for particular examples, such as, Schrodinger operators, Hain–Lust operators, and (if time permits), the Friedrichs model o...

The definition of ordered weighted averaging (OWA) operators and their applications in decision making are reviewed. Also, some generalizations of OWA operators are studied and then, the notion of 2-symmetric OWA operators is introduced. These generalizations are illustrated by some examples.

In this paper, we considered composition operators on weighted Hilbert spaces of analytic functions and  observed that a formula for the  essential norm, gives a Hilbert-Schmidt characterization and characterizes the membership in Schatten-class for these operators. Also, closed range composition operators  are investigated.