Viorel Iftimie

Magnetic Pseudodifferential Operators

In previous papers, a generalization of the Weyl calculus was introduced in connection with the quantization of a particle moving in R n under the influence of a variable magnetic field B. It incorporates phase factors defined by B and reproduces the usual Weyl calculus for B = 0. In the present article we develop the classical pseudodifferential theory of this formalism for the standard symbol classes S m .A mong others, we obtain properties and asymptotic developments for the magnetic symbol multiplication, existence of parametrices, boundedness and positivity results, properties of the magnetic Sobolev spaces. In the case when the vector potential A has all the derivatives of order ≥ 1 bounded, we show that the resolvent and the fractional powers of an elliptic magnetic pseudodifferential operator are also pseudodifferential. As an application, we get a limiting absorption principle and detailed spectral results for self-adjoint operators of the form H = h(Q, Π A ), where h is an elliptic symbol, Q denotes multiplication with the variables Π A = D −A, D is the operator of derivation and A is the vector potential corresponding to a short-range magnetic field.

Wave operators in a multistratified strip

AbstractOne investigates the scattering theory for the positive self-adjoint operatorH=−Δ·ρΔ acting in

Opérateurs différentiels magnétiques : stabilité des trous dans le spectre, invariance du spectre essentiel et applications

\mathcal{H} = L^2 (\Omega )

Uniqueness and Existence of the Integrated Density of States for Schrodinger Operators with Magnetic Field and Electric Potential with Singular Negative Part

with Ω=Ω′ × ℝ and Ω′ a bounded open set in ℝn−1,n≥2. The real-valued function ρ belongs toL∞ (Ω), is bounded from below byc>0 and there exist real-valued functionsρ1 andρ2 inL∞ (Ω) such thatρ −ρj,j=1,2 is a short range perturbation ofρj when (−1)jxn→+∞. One assumesρj=ρ(j) ⊗1R,j=1,2, withρ(j) ∈L∞ bounded from below byc>0. One proves the existence and completeness of the generalized wave operatorsΩj± =s −

Analyse spectrale et complétude asymptotique pour une bande multi-stratifiée perturbée

\mathop {\lim }\limits_{t \to \pm \infty } e^{itH}

The Peierls–Onsager effective Hamiltonian in a complete gauge covariant setting: determining the spectrum

χje−itHj,j=1,2, withHj=−Δ·ρjΔ and χj:Ω →ℝ equal to 1 if (−1)jxn>0 and to 0 if (−1)jxn<0. The ranges ofWj±:=(Ωj±)* are characterized so that