This is a survey of accumulated spectral analysis observations spanning more than a
century, referring to the double layer potential integral equation, also known as Neumann …

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 …

We consider the adjoint double layer potential (Neumann–Poincaré (NP)) operator
appearing in 3-dimensional elasticity. We show that the recent result about the polynomial …

We prove that the space of vector fields on the boundary of a bounded domain with the
Lipschitz boundary in three dimensions is decomposed into three subspaces: elements of …

Abstract For the Neumann-Poincaré (double layer potential) operator in the three-
dimensional elasticity we establish asymptotic formulas for eigenvalues converging to the …

arXiv:2112.05733v1 [math.AP] 10 Dec 2021 Page 1 arXiv:2112.05733v1 [math.AP] 10 Dec
2021 DISCRETE SPECTRUM OF ZERO ORDER PSEUDODIFFERENTIAL OPERATORS …

arXiv:2006.10568v1 [math.SP] 18 Jun 2020 Page 1 arXiv:2006.10568v1 [math.SP] 18 Jun
2020 EIGENVALUE ASYMPTOTICS FOR POLYNOMIALLY COMPACT …

We link Sogge's type $ L^ p $-estimates for eigenfunctions of the Laplacian on compact
manifolds with the problem of providing criteria for the $ r $-nuclearity of Fourier integral …

We consider the Neumann-Poincar'e (double layer potential) operator in 3D elasicity on a
smooth closed surface. Its essential spectrum consists of 3 points. We find the asymptotics of …

For the Neumann-Poincaré (double layer potential) operator in the three-dimensional
elasticity we establish asymptotic formulas for eigenvalues converging to the points of the …