On the boundary convergence of solutions to the Hermite-Schrödinger equation

Peter Sjögren, and J. L. Torrea. "On the boundary convergence of solutions to the Hermite-Schrödinger equation." Colloquium Mathematicae 118.1 (2010): 161-174. <http://eudml.org/doc/283821>.

@article{PeterSjögren2010,
abstract = {In the half-space $ℝ^\{d\} × ℝ₊$, consider the Hermite-Schrödinger equation i∂u/∂t = -Δu + |x|²u, with given boundary values on $ℝ^\{d\}$. 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.},
author = {Peter Sjögren, J. L. Torrea},
journal = {Colloquium Mathematicae},
keywords = {Hermite expansions; Schrödinger equation; Strichartz estimates; boundary convergence},
language = {eng},
number = {1},
pages = {161-174},
title = {On the boundary convergence of solutions to the Hermite-Schrödinger equation},
url = {http://eudml.org/doc/283821},
volume = {118},
year = {2010},
}

TY - JOUR
AU - Peter Sjögren
AU - J. L. Torrea
TI - On the boundary convergence of solutions to the Hermite-Schrödinger equation
JO - Colloquium Mathematicae
PY - 2010
VL - 118
IS - 1
SP - 161
EP - 174
AB - In the half-space $ℝ^{d} × ℝ₊$, consider the Hermite-Schrödinger equation i∂u/∂t = -Δu + |x|²u, with given boundary values on $ℝ^{d}$. 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.
LA - eng
KW - Hermite expansions; Schrödinger equation; Strichartz estimates; boundary convergence
UR - http://eudml.org/doc/283821
ER -