R440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Recent Progress on Landis’ Conjecture
Blair Davey (The City College of New York)
Abstract
In the late 1960s, E.M. Landis made the following conjecture:
If
and
are bounded functions, and
is a solution to
in
that decays like
, then
must be identically zero. In 1992, V. Z. Meshkov disproved this conjecture by constructing bounded functions
\Delta u = V u
and satisfy
.
The result of Meshkov was accompanied by qualitative unique continuation estimates for solutions in
. In 2005, J. Bourgain and C. Kenig quantified Meshkov's unique continuation estimates.These results, and the generalizations that followed, have led to a fairly complete understanding of the complex-valued setting.However, there are reasons to believe that Landis' conjecture may be true in the real-valued setting.We will discuss recent progress towards resolving the real-valued version of Landis' conjecture in the plane.