2021/11/18 by Joachim Toft, Divyang G. Bhimani, Toft, Joachim +3 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2111.09575
openalex publication_date 2021/11/18 · openalex created_date 2022/09/17 · openalex updated_date 2026/07/28
We show 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 the harmonic oscillator propagator when acting on 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 Pilipovic spaces.