Remarks on some dispersive estimates

Yonggeun Cho, Tohru Ozawa, Suxia Xia

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    36 Citations (Scopus)

    Abstract

    In this paper we consider the initial value problem for i∂tu + ω(|r|)u = 0. Under suitable smoothness and growth conditions on ω, we derive dispersive estimates which is the generalization of time decay and Strichartz estimates. We unify and also simplify dispersive estimates by utilizing the Bessel function. Another main ingredient of this paper is to revisit oscillatory integrals of [2].

    Original languageEnglish
    Pages (from-to)1121-1128
    Number of pages8
    JournalCommunications on Pure and Applied Analysis
    Volume10
    Issue number4
    DOIs
    Publication statusPublished - 2011 Jul

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    Keywords

    • Bessel functions
    • Dispersive equations
    • Dispersive estimate
    • Oscillatory integral
    • Strichartz estimate
    • Time decay

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

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