Analytic Smoothing Effect for the Nonlinear Schrödinger Equations Without Square Integrability

Gaku Hoshino; Ryosuke Hyakuna

doi:10.1007/s00041-017-9562-6

Analytic Smoothing Effect for the Nonlinear Schrödinger Equations Without Square Integrability

Gaku Hoshino, Ryosuke Hyakuna

Waseda Research Institute for Science and Engineering

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

3 Citations (Scopus)

Abstract

In this study we consider the Cauchy problem for the nonlinear Schrödinger equations with data which belong to (Formula presented.)(Formula presented.) In particular, we discuss analytic smoothing effect with data which satisfy exponentially decaying condition at spatial infinity in (Formula presented.)(Formula presented.) 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 (Formula presented.).

Original language	English
Pages (from-to)	1-20
Number of pages	20
Journal	Journal of Fourier Analysis and Applications
DOIs	https://doi.org/10.1007/s00041-017-9562-6
Publication status	Accepted/In press - 2017 Sep 15

Keywords

Analytic Hardy space
Analytic smoothing effect
Nonlinear Schrödinger equations

ASJC Scopus subject areas

Analysis
Mathematics(all)
Applied Mathematics

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10.1007/s00041-017-9562-6

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AU - Hyakuna, Ryosuke

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N2 - In this study we consider the Cauchy problem for the nonlinear Schrödinger equations with data which belong to (Formula presented.)(Formula presented.) In particular, we discuss analytic smoothing effect with data which satisfy exponentially decaying condition at spatial infinity in (Formula presented.)(Formula presented.) 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 (Formula presented.).

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KW - Analytic Hardy space

KW - Analytic smoothing effect

KW - Nonlinear Schrödinger equations

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