Lower Lp-Bounds for Scattering Solutions of the Schrödinger Equations

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Abstract

In this article, the asymptotic behavior in time of scattering solutions to the Schrödinger equation is investigated. Under rather natural assumptions, Ln(Rn)-lower bound estimates of the form for with Φ ≠0 are established, where Hcont(H) denotes the continuous spectral subspace of H. This shows that the estimates obtained by the author in [10] are optimal.

Original languageEnglish
Pages (from-to)579-586
Number of pages8
JournalPublications of the Research Institute for Mathematical Sciences
Volume25
Issue number4
DOIs
Publication statusPublished - 1989
Externally publishedYes

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Scattering
Estimate
Asymptotic Behavior
Subspace
Lower bound
Denote
Form

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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title = "Lower Lp-Bounds for Scattering Solutions of the Schr{\"o}dinger Equations",
abstract = "In this article, the asymptotic behavior in time of scattering solutions to the Schr{\"o}dinger equation is investigated. Under rather natural assumptions, Ln(Rn)-lower bound estimates of the form for with Φ ≠0 are established, where Hcont(H) denotes the continuous spectral subspace of H. This shows that the estimates obtained by the author in [10] are optimal.",
author = "Tohru Ozawa",
year = "1989",
doi = "10.2977/prims/1195173182",
language = "English",
volume = "25",
pages = "579--586",
journal = "Publications of the Research Institute for Mathematical Sciences",
issn = "0034-5318",
publisher = "European Mathematical Society Publishing House",
number = "4",

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AU - Ozawa, Tohru

PY - 1989

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AB - In this article, the asymptotic behavior in time of scattering solutions to the Schrödinger equation is investigated. Under rather natural assumptions, Ln(Rn)-lower bound estimates of the form for with Φ ≠0 are established, where Hcont(H) denotes the continuous spectral subspace of H. This shows that the estimates obtained by the author in [10] are optimal.

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JO - Publications of the Research Institute for Mathematical Sciences

JF - Publications of the Research Institute for Mathematical Sciences

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