On the boundary convergence of solutions to the
Hermite–Schrödinger equation
Colloquium Mathematicum, Tome 118 (2010) no. 1, pp. 161-174
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
In the half-space $\mathbb R^d \times \mathbb R_+$, consider the
Hermite–Schrödinger equation $i\partial u/\partial t = -
\Delta u + |x|^2 u$, with given boundary values on $\mathbb R^d$.
We prove
a formula that links the solution of this
problem to that of the classical Schrödinger equation.
It shows that mixed norm estimates for the
Hermite–Schrödinger equation
can be obtained immediately from
those known in the classical case. In one space dimension, we deduce
sharp pointwise convergence results at the boundary by means of this
link.
Keywords:
half space mathbb times mathbb consider hermite schr dinger equation partial partial delta given boundary values mathbb prove formula links solution problem classical schr dinger equation shows mixed norm estimates hermite schr dinger equation obtained immediately those known classical space dimension deduce sharp pointwise convergence results boundary means link
Affiliations des auteurs :
Peter Sjögren 1 ; J. L. Torrea 2
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author = {Peter Sj\"ogren and J. L. Torrea},
title = {On the boundary convergence of solutions to the {
Hermite{\textendash}Schr\"odinger} equation},
journal = {Colloquium Mathematicum},
pages = {161--174},
publisher = {mathdoc},
volume = {118},
number = {1},
year = {2010},
doi = {10.4064/cm118-1-8},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm118-1-8/}
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Peter Sjögren; J. L. Torrea. On the boundary convergence of solutions to the Hermite–Schrödinger equation. Colloquium Mathematicum, Tome 118 (2010) no. 1, pp. 161-174. doi: 10.4064/cm118-1-8
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