We give a proof of that harmonic oscillator propagators and fractional Fourier transforms are essentially the same. We deduce continuity properties and fix time estimates for such operators on modulation spaces, and apply the results to prove Strichartz estimates for such propagators when acting on Pilipović and modulation spaces. Especially we extend some results by Balhara, Cordero, Nicola, Rodino and Thangavelu. We also show that general forms of fractional harmonic oscillator propagators are continuous on suitable Pilipović spaces.

中文翻译：

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Pilipović 和调制空间的分数阶傅立叶变换、谐振子传播器和 Strichartz 估计

我们证明了谐振子传播器和分数傅立叶变换本质上是相同的。我们推导了此类算子在调制空间上的连续性属性并修复了时间估计，并应用结果来证明此类传播器在作用于 Pilipović 和调制空间时的 Strichartz 估计。特别是我们扩展了 Balhara、Cordero、Nicola、Rodino 和 Thangavelu 的一些结果。我们还证明了分数谐振子传播器的一般形式在合适的 Pilipović 空间上是连续的。