What is known today as the Lee-Friedrichs model is characterized by a self-adjoint operator H on a Hilbert space H, which is the sum of two self-adjoint operators H0 and V , such that H,H0 and V have common domain; H0 has absolutely continuous spectrum (of uniform multiplicity) except for the end-point of the semi-bounded from below spectrum, and one or more eigenvalues which may or may not be ...

We study the self-adjoint Pauli operators that can be realized as the square of a self-adjoint Dirac operator and correspond to a magnetic field consisting of a finite number of Aharonov-Bohm solenoids and a regular part, and prove an Aharonov-Casher type formula for the number of zero-modes for these operators. We also see that essentially only one of the Pauli operators are spin-flip invarian...

In this paper, we design some iterative schemes for solving operator equation $ Lu=f $, where $ L:Hrightarrow H $ is a bounded, invertible and self-adjoint operator on a separable Hilbert space $ H $. In this concern,  Richardson and Chebyshev iterative methods are two outstanding as well as long-standing ones. They can be implemented in different ways via different concepts.In this paper...

We present a discrete adjoint version of OpenFOAM obtained by operator overloading which yields, in comparison to continuous adjoint versions, a greater flexibility and robustness. We discuss our implementation and how the discrete adjoint version of OpenFOAM differs from existing continuous implementations. To reduce the inherent memory requirement of discrete adjoint code we introduce a check...

The Hodge theory of the de Rham complex in the setting of the Sobolev topology is studied. As a result, a new elliptic boundaryvalue problem is obtained. Next, the Hodge theory of the @-Neumann problem in the Sobolev topology is studied. A new @-Neumann boundary condition is obtained, and the corresponding subelliptic estimate derived. The classical Hodge theory on a domain in R N+1 (or, more g...

We prove explicitly that to every discrete, semibounded Hamiltonian with constant degeneracy and with finite sum of the squares of the reciprocal of its eigenvalues and whose eigenvectors span the entire Hilbert space there exists a characteristic self-adjoint time operator which is canonically conjugate to the Hamiltonian in a dense subspace of the Hilbert space. Moreover, we show that each ch...

LetA be a ν-vector of self-adjoint, pairwise commuting operators andB a bounded operator of classCn0 (A). We prove a Taylor-like expansion of the commutator [B, f(A)] for a large class of functions f : Rν → R, generalising the one-dimensional result where A is just a self-adjoint operator. This is done using almost analytic extensions and the higher-dimensional Helffer-Sjöstrand formula.

We prove explicitly that to every discrete, semibounded Hamiltonian with constant degeneracy and with finite sum of the squares of the reciprocal of its eigenvalues and whose eigenvectors span the entire Hilbert space there exists a characteristic self-adjoint time operator which is canonically conjugate to the Hamiltonian in a dense subspace of the Hilbert space. Moreover, we show that each ch...

Implicit–explicit multistep methods for nonlinear parabolic equations were recently analyzed in [2, 3, 1]. In these papers the linear operator of the equation is assumed time-independent, self-adjoint and positive definite; then, the linear part is discretized implicitly and the remaining part explicitly. Here we slightly relax the hypotheses on the linear operator by allowing part of it to be ...

We investigate the spectral flows of the hermitian Wilson-Dirac operator in the fundamental and adjoint representations on two ensembles of pure SU(2) gauge field configurations at the same physical volume. We find several background gauge field configurations where the index of the hermitian Wilson-Dirac operator in the adjoint representation is not four times the index in the fundamental repr...