1. CMB Online first
||Injectivity of generalized Wronski maps|
We study linear projections on PlÃ¼cker space whose restriction
to the Grassmannian is a non-trivial branched
When an automorphism of the Grassmannian preserves the fibers,
we show that the Grassmannian is necessarily
of $m$-dimensional linear subspaces in a symplectic vector
space of dimension $2m$, and the linear map is
the Lagrangian involution.
The Wronski map for a self-adjoint linear differential operator
and pole placement map for
symmetric linear systems are natural examples.
Keywords:Wronski map, PlÃ¼cker embedding, curves in Lagrangian Grassmannian, self-adjoint linear differential operator, symmetric linear control system, pole placement map
Categories:14M15, 34A30, 93B55
2. CMB 2005 (vol 48 pp. 405)
||Liouville's Theorem in the Radially Symmetric Case |
We present a very short proof of Liouville's theorem for solutions
to a non-uniformly elliptic radially symmetric equation. The proof uses
the Ricatti equation satisfied by the Dirichlet to Neumann map.