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# 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 Copyright for this article belongs to ELsevier. Hermite operator;Schrodinger equation;Oscillatory semigroup;Regularity Division of Physical & Mathematical Sciences > Mathematics 10 Aug 2005 19 Sep 2010 04:19 http://eprints.iisc.ernet.in/id/eprint/3502

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