We generalize the notion of Lagrangian subspaces to self-orthogonal subspaces with respect to a (skew-)symmetric form, thus characterizing (skew-) self-adjoint and unitary operators by means of self-orthogonal subspaces. By orthogonality preserving mappings, these characterizations can be transferred to abstract boundary value spaces of (skew-)symmetric operators. Introducing the notion of boun...

In this article we consider the zeta regularized determinant of Laplace-type operators on the generalized cone. For arbitrary self-adjoint extensions of a matrix of singular ordinary differential operators modelled on the generalized cone, a closed expression for the determinant is given. The result involves a determinant of an endomorphism of a finite-dimensional vector space, the endomorphism...

We use C *-algebra theory to provide a new method of decomposing the essential spectra of self-adjoint and non-self-adjoint Schrödinger operators in one or more space dimensions.

Spectra of observables in the q-oscillator and q-analogue of the Fourier transform Abstract. Spectra of the position and momentum operators of the Biedenharn-Macfarlane q-oscillator (with the main relation aa + − qa + a = 1) are studied when q > 1. These operators are symmetric but not self-adjoint. They have one-parameter family of self-adjoint extensions. These extensions are derived explicit...

Given, on the Hilbert space H0, the self-adjoint operator B and the skew-adjoint operators C1 and C2, we consider, on the Hilbert space H ≃ D(B)⊕H0, the skew-adjoint operator