Generic simplicity of resonances in obstacle scattering

Resonances and Balls in Obstacle Scattering with Neumann Boundary Conditions

We consider scattering by an obstacle in Rd, d ≥ 3 odd. We show that for the Neumann Laplacian if an obstacle has the same resonances as the ball of radius ρ does, then the obstacle is a ball of radius ρ. We give related results for obstacles which are disjoint unions of several balls of the same radius.

Light scattering by a finite obstacle and fano resonances.

The conditions for observing Fano resonances at elastic light scattering by a single finite-size obstacle are discussed. General arguments are illustrated by consideration of the scattering by a small (relative to the incident light wavelength) spherical obstacle based upon the exact Mie solution of the diffraction problem. The most attention is paid to recently discovered anomalous scattering....

Simplicity of generic Steiner bundles

1 Abstract: A Steiner bundle E on P n has a linear resolution of the form 0 → O(−1) s →O t → E → 0. In this paper we prove that a generic Steiner bundle E is simple if and only if χ(End E) is less or equal to 1. In particular we show that either E is exceptional or it satisfies the inequality t ≤ n+1+ √ (n+1) 2 −4 2 s.

Scattering, Inverse Scattering and Resonances in R

Obstacle Scattering as Seen

We recount some of Ralph Kleinman's scientiic achievements in obstacle scattering for time harmonic waves by reporting on two topics where R.K. and R.K. interacted mathematically. The rst topic is the problem of nonuniqueness for the classical boundary integral equations for the direct scattering problem and the second is the development of numerical methods for the inverse scattering problem.