34 citations · 193 across the 55 of their papers we have counts for
7 papers · 1 filter
Asymptotics for the spectral function on Zoll manifolds
Yaiza Canzani, Jeffrey Galkowski, Blake Keeler
Let be a Zoll manifold, i.e., a smooth, compact, Riemannian manifold without boundary all of whose geodesics are closed with a minimal common period . The positive defin…
Lower bounds for piecewise polynomial approximations of oscillatory functions
Jeffrey Galkowski
We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and h…
The scattering phase: seen at last
Jeffrey Galkowski, Pierre Marchand, Jian Wang +1
The scattering phase, defined as where is the (unitary) scattering matrix, is the analogue of the counting function for eigenvalues when deali…
Classical Wave methods and modern gauge transforms: Spectral Asymptotics in the one dimensional case
Jeffrey Galkowski, Leonid Parnovski, Roman Shterenberg
In this article, we consider the asymptotic behaviour of the spectral function of Schrödinger operators on the real line. Let have the form…
The -FEM applied to the Helmholtz equation with PML truncation does not suffer from the pollution effect
Jeffrey Galkowski, David Lafontaine, Euan A. Spence +1
We consider approximation of the variable-coefficient Helmholtz equation in the exterior of a Dirichlet obstacle using perfectly-matched-layer (PML) truncation; it is well known th…
Logarithmic improvements in the Weyl law and exponential bounds on the number of closed geodesics are predominant
Yaiza Canzani, Jeffrey Galkowski
Let be a smooth compact manifold of dimension without boundary. We introduce the concept of predominance for Riemannian metrics on , a notion analogous to full Lebesgue…
Does the Helmholtz boundary element method suffer from the pollution effect?
Jeffrey Galkowski, Euan A. Spence
In dimensions, accurately approximating an arbitrary function oscillating with frequency requires degrees of freedom. A numerical method for solving the…