Remarks on analytic smoothing effect for the Schrödinger equation

T. Ozawa; K. Yamauchi

doi:10.1007/s00209-008-0334-5

Remarks on analytic smoothing effect for the Schrödinger equation

T. Ozawa, K. Yamauchi^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

We study analytic smoothing effect of solutions to the Schrödinger equation with Cauchy data decaying exponentially at infinity. The domain of analyticity in the space variables of solutions is described under weight conditions on the data in terms of the corresponding supporting function. The domain of analyticity in the time variable is characterized by means of weight conditions of Gaussian type on the data. A generalization of various isometrical identities related to the analytic smoothing effect is introduced.

Original language	English
Pages (from-to)	511-524
Number of pages	14
Journal	Mathematische Zeitschrift
Volume	261
Issue number	3
DOIs	https://doi.org/10.1007/s00209-008-0334-5
Publication status	Published - 2009 Mar
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00209-008-0334-5

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abstract = "We study analytic smoothing effect of solutions to the Schr{\"o}dinger equation with Cauchy data decaying exponentially at infinity. The domain of analyticity in the space variables of solutions is described under weight conditions on the data in terms of the corresponding supporting function. The domain of analyticity in the time variable is characterized by means of weight conditions of Gaussian type on the data. A generalization of various isometrical identities related to the analytic smoothing effect is introduced.",

author = "T. Ozawa and K. Yamauchi",

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AB - We study analytic smoothing effect of solutions to the Schrödinger equation with Cauchy data decaying exponentially at infinity. The domain of analyticity in the space variables of solutions is described under weight conditions on the data in terms of the corresponding supporting function. The domain of analyticity in the time variable is characterized by means of weight conditions of Gaussian type on the data. A generalization of various isometrical identities related to the analytic smoothing effect is introduced.

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DO - 10.1007/s00209-008-0334-5

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JF - Mathematische Zeitschrift

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ER -

Remarks on analytic smoothing effect for the Schrödinger equation

Abstract

ASJC Scopus subject areas

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