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 study second adjointness in the context of tempered admissible representations a real reductive group. Compared to recent result Crisp and Higson, this generalizes from SL2 general group, but specializes only considering representations. also discuss Casselman’s canonical pairing context, relation Bernstein morphisms. Additionally, we take opportunity some relevant functors their relations.

In the canonical approach to Lorentzian Quantum General Relativity in four spacetime dimensions an important step forward has been made by Ashtekar, Isham and Lewandowski some eight years ago through the introduction of a Hilbert space structure which was later proved to be a faithful representation of the canonical commutation and adjointness relations of the quantum field algebra of diffeomor...

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 ...

The non self-adjointness of the radial momentum operator has been noted before by several authors, but the various proofs are incorrect. We give a rigorous proof that the n-dimensional radial momentum operator is not self-adjoint and has no selfadjoint extensions. The main idea of the proof is to show that this operator is unitarily equivalent to the momentum operator on L[(0,∞), dr] which is n...

We contribute to the theory of implications and conjunctions related by adjointness, in multiple-valued logics. We suggest their use in Zadeh s compositional rule of inference, to interpret generalized modus ponens inference schemata. We provide new complete characterizations of implications that distinguish left arguments, implications that satisfy the exchange principle, divisible conjunction...

By using the spherical coordinates in 3+1 dimensions we study the self-adjointness of the Dirac Hamiltonian in an Aharonov-Bohm gauge field of an infinitely thin magnetic flux tube. It is shown that the angular part of the Dirac Hamiltonian requires self-adjoint extensions as well as its radial one. The self-adjoint extensions of the angular part are parametrized by a 2 × 2 unitary matrix. ∗e-m...

We study the adjointness problem for the closed extensions of a general b-elliptic operator A ∈ x Diffmb (M ;E), ν > 0, initially defined as an unbounded operator A : C∞ c (M ;E) ⊂ x L b (M ;E) → xL b (M ;E), μ ∈ R. The case where A is a symmetric semibounded operator is of particular interest, and we give a complete description of the domain of the Friedrichs extension of such an operator.

We introduce here a generalization of the modified Bernstein polynomials for Jacobi weights using the q-Bernstein basis proposed by G.M. Phillips to generalize classical Bernstein Polynomials. The function is evaluated at points which are in geometric progression in ]0, 1[. Numerous properties of the modified Bernstein Polynomials are extended to their q-analogues: simultaneous approximation, p...

The quantization of closed cosmologies makes it necessary to study squared Dirac operators on closed intervals and the corresponding quantum amplitudes. This paper shows that the proof of essential self-adjointness of these second-order elliptic operators is related to Weyl’s limit point criterion, and to the properties of continuous potentials which are positive near zero and are bounded on th...