### ... 1/4

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This...

Hörmander’s famous Fourier multiplier theorem ensures the ${L}_{p}$-boundedness of $F(-{\Delta}_{\mathbb{R}}D)$ whenever $F\in \mathscr{H}\left(s\right)$ for some $s\>\frac{D}{2}$, where we denote by $\mathscr{H}\left(s\right)$ the set of functions satisfying the Hörmander condition for $s$ derivatives. Spectral multiplier theorems are extensions of this result to more general operators $A\ge 0$ and yield the ${L}_{p}$-boundedness of $F\left(A\right)$ provided $F\in \mathscr{H}\left(s\right)$ for some $s$ sufficiently large. The harmonic oscillator $A=-{\Delta}_{\mathbb{R}}+{x}^{2}$ shows that in general $s\>\frac{D}{2}$ is not sufficient even if $A$ has a heat kernel satisfying gaussian estimates. In this paper,...

This article is concerned with estimations from below for the remainder term in Weyl’s law for the spectral counting function of certain rational (2ℓ + 1)-dimensional Heisenberg manifolds. Concentrating on the case of odd ℓ, it continues the work done in part I [21] which dealt with even ℓ.

This article is dedicated to localization of the principal eigenvalue (PE) of the Stokes operator acting on solenoidal vector fields that vanish outside a large random domain modeling the pore space in a cubic block of porous material with disordered micro-structure. Its main result is an asymptotically deterministic lower bound for the PE of the sum of a low compressibility approximation to the Stokes operator and a small scaled random potential term, which is applied to produce a similar bound...

In this paper we prove a maxmin principle for nonlinear nonoverdamped eigenvalue problems corresponding to the characterization of Courant, Fischer and Weyl for linear eigenproblems. We apply it to locate eigenvalues of a rational spectral problem in fluid-solid interaction.