2023/08/02 by Joachim Toft, Divyang G. Bhimani, Ramesh Manna
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Mathematical Analysis and Transform Methods
paper · doi:10.1016/j.acha.2023.101580
openalex publication_date 2023/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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.