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...

We discuss connections between the essential self-adjointness of a symmetric operator and constancy functions which are in kernel adjoint operator. then illustrate this relationship case Laplacians on both manifolds graphs. Furthermore, we Green’s function when it gives non-constant harmonic is square integrable.

We introduce a novel approach for defining a δ′-interaction on a subset of the real line of Lebesgue measure zero which is based on Sturm– Liouville differential expression with measure coefficients. This enables us to establish basic spectral properties (e.g., self-adjointness, lower semiboundedness and spectral asymptotics) of Hamiltonians with δ′-interactions concentrated on sets of complica...

In this article, we mainly study the weighted composition-differentiation operator on Bergman space A?2 and derivative Hardy S12, which characterize complex symmetric Du,?. Moreover, normality self-adjointness of Du,? are also discussed.

We discuss a new simplified proof of the essential self-adjointness for formally self-adjoint differential operators real principal type with null non-trapping condition, previously proved by Vasy (J Spectr Theory 10: 439–461, 2020) and Nakamura-Taira (Ann Henri Lebesgue 4: 1035–1059, 2021). For simplicity, here we second-order cases, i.e., Klein–Gordon-type only.

We prove essential self-adjointness of the spatial part linear Klein-Gordon operator with external potential for a large class globally hyperbolic manifolds. The proof is conducted by fusion new results concerning manifolds, theory weighted Hilbert spaces and related functional analytic advances.

The self-adjointness of an evolution operator corresponding to the model of the flat FRW universe with massless scalar field and cosmological constant quantized in the framework of loop quantum cosmology is studied in the case > 0. It is shown that, for < c 10:3‘ 2 Pl , the operator admits many self-adjoint extensions, each of the purely discrete spectrum. On the other hand for c the operator i...