Distribution des résonances et décroissance de l’énergie locale pour le problème de transmission
Distribution des résonances pour le système de l'élasticité
Distribution laws for integrable eigenfunctions
We determine the asymptotics of the joint eigenfunctions of the torus action on a toric Kähler variety. Such varieties are models of completely integrable systems in complex geometry. We first determine the pointwise asymptotics of the eigenfunctions, which show that they behave like Gaussians centered at the corresponding classical torus. We then show that there is a universal Gaussian scaling limit of the distribution function near its center. We also determine the limit...
Distribution near the real axis of scattering poles generated by a non-hyperbolic periodic ray
Distribution of resonances for convex co-compact hyperbolic surfaces
Distributional asymptotic expansions of spectral functions and of the associated Green kernels.
Does Atkinson-Wilcox Expansion Converges for any Convex Domain?
2000 Mathematics Subject Classification: 35C10, 35C20, 35P25, 47A40, 58D30, 81U40.The Atkinson-Wilcox theorem claims that any scattered field in the exterior of a sphere can be expanded into a uniformly and absolutely convergent series in inverse powers of the radial variable and that once the leading coefficient of the expansion is known the full series can be recovered uniquely through a recurrence relation. The leading coefficient of the series is known as the scattering amplitude or the far...
Domain perturbations, capacity and shift of eigenvalues
After introducing the notion of capacity in a general Hilbert space setting we look at the spectral bound of an arbitrary self-adjoint and semi-bounded operator . If is subjected to a domain perturbation the spectrum is shifted to the right. We show that the magnitude of this shift can be estimated in terms of the capacity. We improve the upper bound on the shift which was given in Capacity in abstract Hilbert spaces and applications to higher order differential operators (Comm. P. D. E., 24:759–775,...
Dubrovin Type Equations for Completely Integrable Systems Associated with a Polynomial Pencil
Dubrovin type equations for the N -gap solution of a completely integrable system associated with a polynomial pencil is constructed and then integrated to a system of functional equations. The approach used to derive those results is a generalization of the familiar process of finding the 1-soliton (1-gap) solution by integrating the ODE obtained from the soliton equation via the substitution u = u(x + λt).
Dynamical Resonances and SSF Singularities for a Magnetic Schrödinger Operator
We consider the Hamiltonian H of a 3D spinless non-relativistic quantum particle subject to parallel constant magnetic and non-constant electric field. The operator H has infinitely many eigenvalues of infinite multiplicity embedded in its continuous spectrum. We perturb H by appropriate scalar potentials V and investigate the transformation of these embedded eigenvalues into resonances. First, we assume that the electric potentials are dilation-analytic with respect to the variable along the magnetic...