Geodesic
On the boundary convergence of solutions to the Hermite–Schrödinger equation
Peter Sjögren 1   ; J. L. Torrea 2
1 Mathematical Sciences University of Gothenburg SE-412 96 Göteborg, Sweden and Mathematical Sciences Chalmers SE-412 96 Göteborg, Sweden
2 Departamento de Matemáticas and ICMAT CSIC-UAM-UCM-UC3M Facultad de Ciencias Universidad Autónoma de Madrid 28049 Madrid, Spain
Colloquium Mathematicum, Tome 118 (2010) no. 1, pp. 161-174 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm118-1-8
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

Peter Sjögren  1   ; J. L. Torrea  2

1 Mathematical Sciences University of Gothenburg SE-412 96 Göteborg, Sweden and Mathematical Sciences Chalmers SE-412 96 Göteborg, Sweden
2 Departamento de Matemáticas and ICMAT CSIC-UAM-UCM-UC3M Facultad de Ciencias Universidad Autónoma de Madrid 28049 Madrid, Spain 
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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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