Asymptotic distribution of resonances for convex obstacles

Resonances for Obstacles in Hyperbolic Space

We consider scattering by star-shaped obstacles in hyperbolic space and show that resonances satisfy a universal bound Imλ ≤ − 2 which is optimal in dimension 2. In odd dimensions we also show that Imλ ≤ −μρ for a universal constant μ, where ρ is the (hyperbolic) diameter of the obstacle; this gives an improvement for small obstacles. In dimensions 3 and higher the proofs follow the classical v...

Asymptotic Distribution of Divergence Measure with Applications

Asymptotic Approximation of Convex Curves

L. Fejes Tóth gave asymptotic formulae as n → ∞ for the distance between a smooth convex disc and its best approximating inscribed or circumscribed polygons with at most n vertices, where the distance is in the sense of the symmetric difference metric. In this paper these formulae are extended by specifying the second terms of the asymptotic expansions. Tools are from affine differential geometry.

Asymptotic distribution of eigenvalues of the elliptic operator system

Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.

Asymptotic and Numerical Techniques for Resonances of Thin Photonic Structures

We consider the problem of calculating resonance frequencies and radiative losses of an optical resonator. The optical resonator is in the form of a thin membrane with variable dielectric properties. This work provides two very different approaches for doing such calculations. The first is an asymptotic method which exploits the small thickness and high index of the membrane. We derive a limiti...