On Distributions of Self-Adjoint Extensions of Symmetric Operators

Commuting Self-Adjoint Extensions of Symmetric Operators Defined from the Partial Derivatives

We consider the problem of finding commuting self-adjoint extensions of the partial derivatives { 1 i ∂ ∂xj : j = 1, . . . , d } with domain C c (Ω) where the self-adjointness is defined relative to L (Ω), and Ω is a given open subset of R. The measure on Ω is Lebesgue measure on R restricted to Ω. The problem originates with I.E. Segal and B. Fuglede, and is difficult in general. In this paper...

Self Adjoint Extensions of Phase and Time Operators

It is shown that any real and even function of the phase (time) operator has a self-adjoint extension and its relation to the general phase operator problem is analyzed. Typeset using REVTEX E-mail: [email protected] E-mail: [email protected] E-mail: [email protected]

Self-adjoint Extensions of Restrictions

We provide, by a resolvent Krĕın-like formula, all selfadjoint extensions of the symmetric operator S obtained by restricting the self-adjoint operator A : D(A) ⊆ H → H to the dense, closed with respect to the graph norm, subspace N ⊂ D(A). Neither the knowledge of S∗ nor of the deficiency spaces of S is required. Typically A is a differential operator and N is the kernel of some trace (restric...

Self-adjoint Difference Operators and Symmetric Al-salam–chihara Polynomials

The symmetric Al-Salam–Chihara polynomials for q > 1 are associated with an indeterminate moment problem. There is a self-adjoint second order difference operator on l(Z) to which these polynomials are eigenfunctions. We determine the spectral decomposition of this self-adjoint operator. This leads to a class of discrete orthogonality measures, which have been obtained previously by Christianse...

On Families of Self Adjoint Operators