3 papers
math.SG2009
A Simple Proof of Unique Continuation for J-holomorphic Curves
Michael VanValkenburgh
In this expository paper, we prove strong unique continuation for J-holomorphic curves by first giving a simple proof of Aronszajn's theorem in the special case of the two-dimensio…
quant-ph2009
Manipulation of Semiclassical Laguerre-Gaussian Modes: a Model Case
Michael VanValkenburgh
We continue the study, from a semiclassical viewpoint, of Calvo and Picon's operators, as manipulating photon states in quantum communication. In a previous paper, we defined a one…
math.AP2008
Exponential Lower Bounds for Quasimodes of Semiclassical Schrödinger Operators
Michael VanValkenburgh
We prove quantitative unique continuation results for the semiclassical Schrodinger operator on smooth, compact domains. These take the form of exponentially decreasing (in h) loca…