Related papers: The trace formula for a point scatterer on a hyper…

We consider the case of scattering of several obstacles in $\mathbb{R}^d$ for $d \geq 2$. In this setting the absolutely continuous part of the Laplace operator $\Delta$ with Dirichlet boundary conditions and the free Laplace operator…

Let $f$ be a smooth symplectic diffeomorphism of $\mathbb{R}^2$ admitting a (non-split) separatrix associated to a hyperbolic fixed point. We prove that if $f$ is a perturbation of the time-1 map of a symplectic autonomous vector field,…

The trace formula is a versatile tool for computing sums of spectral data across families of automorphic forms. Using specialized test functions, one can treat small families with refined spectral properties. This has proven fruitful in…

In this paper we study the behaviour of the continuous spectrum of the Laplacian on a complete Riemannian manifold of bounded curvature under perturbations of the metric. The perturbations that we consider are such that its covariant…

We study the behavior of a point particle incident from the left on a slab of a randomly diluted triangular array of circular scatterers. Various scattering properties, such as the reflection and transmission probabilities and the…

We present the first example of the Selberg type zeta function for noncompact higher rank locally symmetric spaces. We study certain Selberg type zeta functions and Ruelle type zeta functions attached to the Hilbert modular group of a real…

We study the Laplacian perturbed by two delta potentials on a two-dimensional flat torus. There are two types of eigenfunctions for this operator: old, or unperturbed eigenfunctions which are eigenfunctions of the standard Laplacian, and…

We consider a vector-Laplace problem posed on a 2D surface embedded in a 3D domain, which results from the modeling of surface fluids based on exterior Cartesian differential operators. The main topic of this paper is the development and…

This paper introduces a boundary integral equation for time-harmonic electromagnetic scattering by composite dielectric objects. The formulation extends the classical M\"uller equation to composite structures through the global multi-trace…

The paper is devoted to investigation of the spectrum of a perturbed Laplace-Beltrami operator on manifolds with closed geodesics of the same length and where metric is a perturbation of the metric of the unit sphere. As the result, we give…

We give a criterion of asymptotic completeness and provide a representation of the scattering matrix for the scattering couple $(A_{0},A)$, where $A_{0}$ and $A$ are semi-bounded self-adjoint operators in $L^{2}(M,{\mathscr B},m)$ such that…

Scattering on the ${\cal PT}$-symmetric Coulomb potential is studied along a U-shaped trajectory circumventing the origin in the complex $x$ plane from below. This trajectory reflects ${\cal PT}$ symmetry, sets the appropriate boundary…

The local trace formula gives strong relations between two types of invariant distributions on a reductive group defined over a local field: orbital integrals and characters of representations. For connected reductive groups, the formula…

For a class of manifolds that includes quotients of real hyperbolic space by a convex co-compact discrete group, we show that the resonances of the meromorphically continued resolvent kernel for the Laplacian coincide, with multiplicities,…

We consider the Laplacian with a delta potential (a "point scatterer") on an irrational torus, where the square of the side ratio is diophantine. The eigenfunctions fall into two classes ---"old" eigenfunctions (75%) of the Laplacian which…

We derive, and discuss the properties of, a symplectic map for the dynamics of bodies on nearly parabolic orbits. The orbits are perturbed by a planet on a circular, coplanar orbit interior to the pericenter of the parabolic orbit. The map…

Let G be a reductive algebraic group over Q, and suppose that Gamma is an arithmetic subgroup of G(R) defined by congruence conditions. A basic problem in arithmetic is to determine the multiplicities of discrete series representations in…

Using the Selberg trace formula, we show that for a hyperbolic 2-orbifold, the spectrum of the Laplacian acting on functions determines, and is determined by, the following data: the volume; the total length of the mirror boundary; the…

We study the formation of clusters of passive Lagrangian tracers in a non-smooth turbulent flow in a flat free-slip surface as a model for particle dynamics on free surfaces. Single particle and pair dispersion show different behavior for…

The discrete Laplacian on Euclidean triangulated surfaces is a well-established notion. We introduce discrete Laplacians on spherical and hyperbolic triangulated surfaces. On the one hand, our definitions are close to the Euclidean one in…