On sharp Strichartz inequalities in low dimensions

Recently, Foschi gave a proof of a sharp Strichartz inequality in one and two dimensions. In this paper, a new representation in terms of an orthogonal projection operator is obtained for the space-time norm of solutions of the free Schrödinger equation in dimensions one and two. As a consequence, t...

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Bibliographic Details
Published in:International Mathematics Research Notices 2006, Vol.2006
Main Authors: Hundertmark, Dirk, Zharnitsky, Vadim
Format: Article
Language:English
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Summary:Recently, Foschi gave a proof of a sharp Strichartz inequality in one and two dimensions. In this paper, a new representation in terms of an orthogonal projection operator is obtained for the space-time norm of solutions of the free Schrödinger equation in dimensions one and two. As a consequence, the sharp Strichartz inequality follows from the elementary property that orthogonal projections do not increase the norm.
ISSN:1073-7928
1687-1197
1687-0247
DOI:10.1155/IMRN/2006/34080