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

Colloquium Mathematicae (2010)

- Volume: 118, Issue: 1, page 161-174
- ISSN: 0010-1354

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topPeter 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 -

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