Schrodinger equation and the oscillatory semigroup for the Hermite operator

Nandakumaran, AK and Ratnakumar, PK (2005) Schrodinger equation and the oscillatory semigroup for the Hermite operator. In: Journal of Functional Analysis, 224 (2). pp. 371-385.

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Abstract

We discuss the regularity of the oscillatory semigroup $e^{itH}$, where $H= -\Delta \mid x \mid ^{2}$ is the n-dimensional Hermite operator. The main result is a Strichartz-type estimate for the oscillatory semigroup $e^{itH}$ in terms of the mixed $L^{P}$ spaces. The result can be interpreted as the regularity of solution to the Schrodinger equation with potential $V(X) = \mid x \mid ^{2}$.

Item Type:	Journal Article
Publication:	Journal of Functional Analysis
Publisher:	Academic Press Inc Elsevier Science
Additional Information:	Copyright for this article belongs to ELsevier.
Keywords:	Hermite operator;Schrodinger equation;Oscillatory semigroup;Regularity
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	10 Aug 2005
Last Modified:	19 Sep 2010 04:19
URI:	http://eprints.iisc.ac.in/id/eprint/3502

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