Hardy type inequalities with exponential weights for a class of convolution operators

In this paper we consider operators of the form H=λ(-i∇), with λ analytic in a strip and with some specific growth conditions at infinity, and prove Hardy type estimates in L ²(ℝ ⁿ ) with exponential weights. In fact we extend our previous results [19] from bounded analytic functions on a strip to analytic functions with polynomial growth in that strip.     

Weighted Estimations from a Conjugate Operator

In this Letter we develop a general procedure leading from a Mourre-type estimation for a given self-adjoint operator H to a Hardy-type weighted inequality. We use this method in order to prove exponential decay for eigenvectors of a large class of perturbations of operators of convolution with bounded analytic functions.     

On the markoff property for the free Euclidean electromagnetic field

We prove that the free Euclidean electromagnetic field, as constructed by L. Gross in [2], has the Markoff property.     

On Fréchet–Hilbert algebras

We consider Hilbert algebras with a supplementary Fréchet topology and get various extensions of the algebraic structure by using duality techniques. In particular we obtain optimal multiplier-type involutive algebras which in applications are large enough to be of significant practical use. The setting covers many situations arising from quantization rules, as those involving square-integrable families of bounded operators     

Propagation Properties for Schrödinger Operators Affiliated with Certain C*-Algebras

We consider anisotropic Schrödinger operators H = -D + V H = -{\Delta} + V in L²(\mathbbRⁿ) L^{2}(\mathbb{R}^n) . To certain asymptotic regions F we assign asymptotic Hamiltonians H_F such that (a) s(H_F) ì s_ess(H) \sigma(H_F) \subset \sigma_{\textrm{ess}}(H) , (b) states with energies not belonging to s(H_F) \sigma(H_F) do not propagate into a neighbourhood of F under the evolution group defined by H. The proof relies on C*-algebra techniques. We can treat in particular potentials that tend asymptotically to different periodic functions in different cones, potentials with oscillation that decays at infinity, as well as some examples considered before by Davies and Simon in [4].     

A boundary value problem related to the Ginzburg-Landau model

We analyze the Ginzburg-Landau equation for a superconductor in the case of a 2-dimensional model: a cylindrical conductor with a magnetic field parallel to the axis. This amounts to find the extrema of the free energy

A-Priori Decay for Eigenfunction of Perturbed Periodic Schrödinger Operators

. Recently Neumayr and Metzner [1] have shown that the connected N-point density-correlation functions of the two-dimensional and the one-dimensional Fermi gas at one-loop order generically (i.e.for nonexceptional energy-momentum configurations) vanish/are regular in the small momentum/small energy-momentum limits. Their result is based on an explicit analysis in the sequel of the results of Feldman et al. [2]. In this note we use Ward identities to give a proof of the same fact - in a considerably shortened and simplified way - for any dimension of space.     

Characterization of lysozyme films produced by matrix assisted pulsed laser evaporation (MAPLE)

Thin lysozyme films of thickness up to more than 100 nm have been produced in a dry environment by MAPLE (matrix assisted pulsed laser evaporation) from a water ice matrix. Analysis of the films demonstrates that a significant part of the lysozyme molecules is transferred to the substrate without decomposition and that the protein activity is preserved. The film deposition rate for 1 wt% lysozyme has a maximum at 2 J/cm² of about 1 ng/cm² per laser shot. During the film production the deposition rate is constant without any sign of depletion or accumulation effects in the water ice target or in the growing film. Scanning electron microscopy (SEM) images demonstrate that the silicon substrate is completely covered by lysozyme films thicker than 100 nm. Deposition was also made from a target with pressed (100%) solid lysozyme, but the deposition was difficult to handle and with a much slower rate than that from a water ice matrix.     

Some Propagation Properties of the Iwatsuka Model

In this paper we study a two dimensional magnetic field Schr?dinger Hamiltonian introduced in [7]. This model has some interesting propagation properties, as conjectured in [2] and at the same time is a special case of the class of analytically decomposable Hamiltonians [5]. Our aim is to start from a conjugate operator, intimately related to the band structure of the Hamiltonian and to prove existence of an asymptotic velocity in one spatial direction and a theorem giving minimal and maximal velocity bounds for the propagation associated to the Hamiltonian. A simple example of this model, with a very simple conjugate operator, has been given in [9]. At the same time, by using the Virial Theorem, we obtain a generalisation of the hypothesis in [7]. Received: 12 February 1997 / Accepted: 26 February 1997