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Microlocal dispersive smoothing for the Schrödinger equation


Craig, W; Kappeler, T; Strauss, W (1995). Microlocal dispersive smoothing for the Schrödinger equation. Communications on Pure and Applied Mathematics, 48(8):769-860.

Abstract

This paper establishes a connection between the microlocal smoothness of solutions of the initial value problem for Schrödinger's equation and the global behavior of bicharacteristics of the principal symbol. In particular, localized initial data gives rise to solutions which are microlocally smooth at all points which are not trapped backwards by the bicharacteristic flow. The origin of the phenomenon is in the dispersive nature of the equation. The results imply microlocal regularity properties of the fundamental solution. ©1995 John Wiley & Sons. Inc.

Abstract

This paper establishes a connection between the microlocal smoothness of solutions of the initial value problem for Schrödinger's equation and the global behavior of bicharacteristics of the principal symbol. In particular, localized initial data gives rise to solutions which are microlocally smooth at all points which are not trapped backwards by the bicharacteristic flow. The origin of the phenomenon is in the dispersive nature of the equation. The results imply microlocal regularity properties of the fundamental solution. ©1995 John Wiley & Sons. Inc.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1995
Deposited On:18 Feb 2010 12:21
Last Modified:05 Apr 2016 13:27
Publisher:Wiley-Blackwell
ISSN:0010-3640
Publisher DOI:https://doi.org/10.1002/cpa.3160480802
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1361016
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0856.35106

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