Series expansions of the layer potential operators using the Faber polynomials and their applications to the transmission problem

Y Jung, M Lim - SIAM Journal on Mathematical Analysis, 2021 - SIAM
We consider the conductivity transmission problem in two dimensions with a simply
connected inclusion of arbitrary shape. It is well known that the solvability of the transmission …

Elastodynamical resonances and cloaking of negative material structures beyond quasistatic approximation

H Li, H Liu, J Zou - Studies in Applied Mathematics, 2023 - Wiley Online Library
Given the flexibility of choosing negative elastic parameters, we construct material structures
that can induce two resonance phenomena, referred to as the elastodynamical resonances …

[PDF][PDF] SPECTRAL PROPERTIES OF THE NEUMANN-POINCAR E OPERATOR AND CLOAKING BY ANOMALOUS LOCALIZED RESONANCE: A REVIEW

S FUKUSHIMA, YG JI, H KANG… - Journal of the Korean …, 2023 - ksiam.org
This is a review paper on recent development on the spectral theory of the Neumann-
Poincaré operator. The topics to be covered are convergence rate of eigenvalues of the …

Dyson gas on a curved contour

P Wiegmann, A Zabrodin - Journal of Physics A: Mathematical …, 2022 - iopscience.iop.org
We introduce and study a model of a logarithmic gas with inverse temperature β on an
arbitrary smooth closed contour in the plane. This model generalizes Dyson's gas (the β …

The discrete spectrum of the Neumann-Poincaré operator in 3D elasticity

G Rozenblum - Journal of Pseudo-Differential Operators and …, 2023 - Springer
Abstract For the Neumann-Poincaré (double layer potential) operator in the three-
dimensional elasticity we establish asymptotic formulas for eigenvalues converging to the …

Spectral geometry and analysis of the Neumann-Poincaré operator, a review

H Kang - Recent progress in mathematics, 2022 - Springer
Abstract The Neumann-Poincaré operator is an integral operator defined on the boundary of
a bounded domain. The history of research on it goes back to the era of the mathematicians …

The quasi-static plasmonic problem for polyhedra

M de León-Contreras, KM Perfekt - Mathematische Annalen, 2023 - Springer
We characterize the essential spectrum of the plasmonic problem for polyhedra in R 3. The
description is particularly simple for convex polyhedra and permittivities ϵ<-1. The …

Comparison of integral equations for the Maxwell transmission problem with general permittivities

J Helsing, A Karlsson, A Rosén - Advances in Computational Mathematics, 2021 - Springer
Two recently derived integral equations for the Maxwell transmission problem are compared
through numerical tests on simply connected axially symmetric domains for non-magnetic …

[PDF][PDF] Eigenvalue asymptotics for polynomially compact pseudodifferenial operators and applications

G Rozenblum - arXiv preprint arXiv:2006.10568, 2020 - arxiv.org
arXiv:2006.10568v1 [math.SP] 18 Jun 2020 Page 1 arXiv:2006.10568v1 [math.SP] 18 Jun
2020 EIGENVALUE ASYMPTOTICS FOR POLYNOMIALLY COMPACT …

Carleman factorization of layer potentials on smooth domains

K Ando, H Kang, Y Miyanishi, M Putinar - arXiv preprint arXiv:2403.19033, 2024 - arxiv.org
One of the unexplored benefits of studying layer potentials on smooth, closed hypersurfaces
of Euclidean space is the factorization of the Neumann-Poincar\'e operator into a product of …