On decomposition of operators having Γ_3 as a spectral set

Spectral decomposition of Bell’s operators for qubits

The spectral decomposition is given for the N-qubit Bell operators with two observables per qubit. It is found that the eigenstates (when non-degenerate) are N-qubit GHZ states even for those operators that do not allow the maximal violation of the corresponding inequality. We present two applications of this analysis. In particular, we discuss the existence of pure entangled states that do not...

On spectral decomposition of unbounded operators and Gelfand’s theorem

In this paper we are interested in spectral decomposition of an unbounded operator with discrete spectrum. We show that if A generates a polynomially bounded n-times integrated group whose spectrum set σ(A) = {iλk; k ∈ Z } is discrete and satisfies ∑ 1 |λk|δ k < ∞ (n and l nonnegative integers), then there exists projectors (Pk)k∈Z∗ such that ∑ Pkx = x (x ∈ D(A)), where δk = min ( |λk+1 − λk| 2...

Set Operator Decomposition and Conditionally Translation Invariant Elementary Operators

In the first part, we recall the axiomatic definition of the elementary morphological operators (dilations, erosions, anti–dilations and anti–erosions) and their characterization in the case of Boolean lattices. This characterization is used to derive the set operator decompositions from the general decompositions of operators between complete lattices. In the second part, we define the notions...

A new algorithm for solving Van der Pol equation based on piecewise spectral Adomian decomposition ‎method‎

‎‎In this article‎, ‎a new method is introduced to give approximate solution to Van der Pol equation‎. ‎The proposed method is based on the combination of two different methods‎, ‎the spectral Adomian decomposition method (SADM) and piecewise method‎, ‎called the piecewise Adomian decomposition method (PSADM)‎. ‎The numerical results obtained from the proposed method show that this method is an...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators