Wave front set defined by wave packet transform and its application

Kato, Keiichi; Kobayashi, Masaharu; Ito, Shingo

doi:10.2969/aspm/06410417

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Introduction 1motivation: Homogeneous Wavefront Sets On Eucl...1

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“…Gabor wavefront sets are studied in Cordero, Nicola and Rodino [3], Pravda-Starov, Rodino and Wahlberg [19]. Other study by Gabor transforms is in Kato, Kobayashi and S. Ito [10,11]. Another concept of wavefront sets is a quadratic scattering wavefront set, which is studied by Wunsch [24].…”

Section: Introduction 1motivation: Homogeneous Wavefront Sets On Eucl...mentioning

confidence: 99%

Propagation of singularities under Schrödinger equations on manifolds with ends

Fukushima¹

2022

Preprint

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We prove a microlocal smoothing effect of Schrödinger equations on manifolds. We employ radially homogeneous wavefront sets introduced by Ito and Nakamura (Amer. J. Math., 2009). In terms of radially homogeneous wavefront sets, we can apply our theory to both of asymptotically conical and hyperbolic manifolds. We relate wavefront sets in initial states to radially homogeneous wavefront sets in states after a time development. We also prove a relation between radially homogeneous wavefront sets and homogeneous wavefront sets and prove a special case of Nakamura (2005).

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