Abstract

AbstractIn this note, we consider the estimate of solutions to Schrödinger equations with quadratic and sub-quadratic potentials. M. Kobayashi, S. Ito and the author have shown the estimate of solutions to Schrödinger equations with quadratic potentials in modulation spaces M p, p and the estimate with linear and sub-linear potentials in modulation spaces M p, q. Here we give a simple proof for the estimate of solutions to Schrödinger equations with linear and sub-linear potentials in modulation spaces M p, q.KeywordsSchrdinger equationsModulation spacesAdapted a priori estimatesWave-packet transform

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