Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 154, pp. 116.
Global representations of the Heat and Schrodinger equation with
singular potential
Jose A. Franco, Mark R. Sepanski
Abstract:
The ndimensional Schrodinger equation with a singular potential
is studied.
Its solution space is studied as a global representation of
. A special subspace of solutions
for which the action globalizes is constructed via nonstandard
induction outside the semisimple category. The space of Kfinite
vectors is calculated, obtaining conditions for
so that this
space is nonempty. The direct sum of solution spaces over such admissible
values of
is studied as a representation of the (2n+1)dimensional
Heisenberg group.
Submitted February 28, 2013. Published July 2, 2013.
Math Subject Classifications: 22E70, 35Q41.
Key Words: Schr\"{o}dinger equation; heat equation; singular potential;
Lie theory; \hfill\break\indent representation theory; globalization
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Jose A. Franco
University of North Florida
1 UNF Drive, Jacksonville, FL 32082, USA
email: jose.franco@unf.edu


Mark R. Sepanski
Baylor University,
One Bear Place # 97328
Waco, TX 76798, USA
email: mark_sepanski@baylor.edu

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