24 citations · 94 across the 24 of their papers we have counts for
16 papers · 1 filter
Eigenfunction asymptotics and nodal domain estimates for dumbbell domains
Thomas Beck, Yaiza Canzani, Jeremy L. Marzuola
We study the nodal structure of Neumann eigenfunctions on planar dumbbell domains as the width of the neck joining two fixed end domains tends to zero. Under simplicity and non-deg…
Stability of spectral partitions with corners
Gregory Berkolaiko, Yaiza Canzani, Graham Cox +2
A spectral minimal partition of a manifold is a decomposition into disjoint open sets that minimizes a spectral energy functional. While it is known that bipartite minimal partitio…
Homology of spectral minimal partitions
Gregory Berkolaiko, Yaiza Canzani, Graham Cox +1
A spectral minimal partition of a manifold is its decomposition into disjoint open sets that minimizes a spectral energy functional. It is known that bipartite spectral minimal par…
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 eigenfunction restrictions in lacunary regions
Yaiza Canzani, John A. Toth
Let be a compact, smooth Riemannian manifold and be a sequence of -normalized Laplace eigenfunctions that has a localized defect measure in the sense tha…
Quantitative bounds on Impedance-to-Impedance operators with applications to fast direct solvers for PDEs
Thomas Beck, Yaiza Canzani, Jeremy L. Marzuola
We prove quantitative norm bounds for a family of operators involving impedance boundary conditions on convex, polygonal domains. A robust numerical construction of Helmholtz scatt…
Weyl remainders: an application of geodesic beams
Yaiza Canzani, Jeffrey Galkowski
We obtain new quantitative estimates on Weyl Law remainders under dynamical assumptions on the geodesic flow. On a smooth compact Riemannian manifold of dimension , let…
Growth of high norms for eigenfunctions: an application of geodesic beams
Yaiza Canzani, Jeffrey Galkowski
This work concerns norms of high energy Laplace eigenfunctions, , . In 1988, Sogge gave optimal estimates on the growth of f…
Nodal line estimates for the second Dirichlet eigenfunction
Thomas Beck, Yaiza Canzani, Jeremy L. Marzuola
We study the nodal curves of low energy Dirichlet eigenfunctions in generalized curvilinear quadrilaterals. The techniques can be seen as a generalization of the tools developed by…
Eigenfunction concentration via geodesic beams
Yaiza Canzani, Jeffrey Galkowski
In this article we develop new techniques for studying concentration of Laplace eigenfunctions as their frequency, , grows. The method consists of controlling by…
Improvements for eigenfunction averages: An application of geodesic beams
Yaiza Canzani, Jeffrey Galkowski
Let be a smooth, compact Riemannian manifold and an -normalized sequence of Laplace eigenfunctions, . Given a smooth submanifold $H \subset…
On the growth of eigenfunction averages: microlocalization and geometry
Yaiza Canzani, Jeffrey Galkowski
Let be a smooth, compact Riemannian manifold and an -normalized sequence of Laplace eigenfunctions, . Given a smooth submanifold $H \subset M…
Averages of eigenfunctions over hypersurfaces
Yaiza Canzani, Jeffrey Galkowski, John A. Toth
Let be a compact, smooth, Riemannian manifold and an -normalized sequence of Laplace eigenfunctions with defect measure . Let be a smooth hypersurfa…
Topology and nesting of the zero set components of monochromatic random waves
Yaiza Canzani, Peter Sarnak
This paper is dedicated to the study of the topologies and nesting configurations of the components of the zero set of monochromatic random waves. We prove that the probability of…
C-infinity Scaling Asymptotics for the Spectral Function of the Laplacian
Yaiza Canzani, Boris Hanin
This article concerns new off-diagonal estimates on the remainder and its derivatives in the pointwise Weyl law on a compact n-dimensional Riemannian manifold. As an application, w…
Nodal sets of Schrödinger eigenfunctions in forbidden regions
Yaiza Canzani, John Toth
This note concerns the nodal sets of eigenfunctions of semiclassical Schrödinger operators acting on compact, smooth, Riemannian manifolds, with no boundary. We prove that if H is…