Zobrazeno 1 - 10
of 140
pro vyhledávání: '"Christianson, Hans"'
Autor:
Christianson, Hans, Toth, John
For sequences of quantum ergodic eigenfunctions, we define the quantum flux norm associated to a codimension $1$ submanifold $\Sigma$ of a non-degenerate energy surface. We prove restrictions of eigenfunctions to $\Sigma$, realized using the quantum
Externí odkaz:
http://arxiv.org/abs/2404.02296
Autor:
Christianson, Hans, Toth, John A.
Let $\Omega$ be a piecewise-smooth, bounded convex domain in $\R^2$ and consider $L^2$-normalized Neumann eigenfunctions $\phi_{\lambda}$ with eigenvalue $\lambda^2$. Our main result is a small-scale {\em non-concentration} estimate: We prove that fo
Externí odkaz:
http://arxiv.org/abs/2309.10875
We introduce the control conditions for 0th order pseudodifferential operators $\mathbf{P}$ whose real parts satisfy the Morse--Smale dynamical condition. We obtain microlocal control estimates under the control conditions. As a result, we show that
Externí odkaz:
http://arxiv.org/abs/2303.06443
Autor:
Christianson, Hans, Pezzi, Daniel
In this paper, we continue the study of eigenfunctions on triangles initiated by the first author in \cite{Chr-tri} and \cite{Chr-simp}. The Neumann data of Dirichlet eigenfunctions on triangles enjoys an equidistribution law, being equidistributed o
Externí odkaz:
http://arxiv.org/abs/2301.03555
Autor:
Christianson, Hans, Pezzi, Daniel
Publikováno v:
In Journal of Differential Equations 25 October 2024 407:153-180
Autor:
Christianson, Hans, Toth, John A.
Let $(\Omega,g)$ be a piecewise-smooth, bounded convex domain in $\R^2$ and consider $L^2$-normalized Neumann eigenfunctions $\phi_{\lambda}$ with eigenvalue $\lambda^2$ and $u_{\lambda}:= \phi_{\lambda} |_{\partial \Omega}$ the associated Dirichlet
Externí odkaz:
http://arxiv.org/abs/2012.15237
Autor:
Christianson, Hans, Muckerman, Dylan
The purpose of this paper is to study the effect of conformal perturbations on the local smoothing effect for the Schr\"odinger equation on surfaces of revolution. The paper \cite{ChWu-lsm} studied the Schr\"odinger equation on surfaces of revolution
Externí odkaz:
http://arxiv.org/abs/2007.00078
Autor:
Christianson, Hans, Nowak, Derrick
Geodesic trapping is an obstruction to dispersive estimates for solutions to the Schr\"odinger equation. Surprisingly little is known about solutions to the Schr\"odinger equation on manifolds with degenerate trapping, since the conditions for degene
Externí odkaz:
http://arxiv.org/abs/2005.13591
Autor:
Carpenter, Sarah, Christianson, Hans
We consider the Schr\"{o}dinger equation $(i\partial_t+\Delta)u=0$ on an $n$-dimensional simplex with Dirichlet boundary conditions. We use a commutator argument along with integration by parts to obtain an observability asymptotic for any one face o
Externí odkaz:
http://arxiv.org/abs/2005.11287
Autor:
Christianson, Hans, Lu, Ziqing
In this paper, we consider the wave equation on an n-dimensional simplex with Dirichlet boundary conditions. Our main result is an asymptotic observability identity from any one face of the simplex. The novel aspects of the result are that it is a la
Externí odkaz:
http://arxiv.org/abs/2004.01748