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Analytic Smoothing Effect for the Nonlinear Schrödinger Equations Without Square Integrability

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Abstract

In this study we consider the Cauchy problem for the nonlinear Schrödinger equations with data which belong to \(L^p,\)\(1<p<2.\) In particular, we discuss analytic smoothing effect with data which satisfy exponentially decaying condition at spatial infinity in \(L^p,\)\(1<p<2.\) We construct solutions in the function space of analytic vectors for the Galilei generator and the analytic Hardy space with the phase modulation operator based on \(L^{p}\).

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Acknowledgements

The authors would like to thank the anonymous referees for their helpful comments and suggestions.

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Author notes

  1. Gaku Hoshino

    Present address: Osaka University, Toyonaka, Osaka, 560-0043, Japan

Authors and Affiliations

  1. Waseda University, Shinjuku, Tokyo, 169-8555, Japan

    Gaku Hoshino & Ryosuke Hyakuna

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  1. Gaku Hoshino
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  2. Ryosuke Hyakuna
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Correspondence to Gaku Hoshino.

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Communicated by Luis Vega.

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Hoshino, G., Hyakuna, R. Analytic Smoothing Effect for the Nonlinear Schrödinger Equations Without Square Integrability. J Fourier Anal Appl 24, 1661–1680 (2018). https://doi.org/10.1007/s00041-017-9562-6

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  • DOI: https://doi.org/10.1007/s00041-017-9562-6

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