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

Peter Sjögren (Institutionen för matematiska vetenskaper) ; José Luis Torrea
Colloquium Mathematicum (0010-1354). Vol. 118 (2010), p. 161-174.
[Artikel, refereegranskad vetenskaplig]

In a half-space we consider the Hermite Schrödinger equation with given boundary values. 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.

Nyckelord: Hermite expansions, Schrödinger equation, Strichartz estimates, boundary convergence



Denna post skapades 2009-10-29. Senast ändrad 2014-09-29.
CPL Pubid: 101018

 

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