Fractional Fourier transforms, harmonic oscillator propagators and Strichartz estimates on Pilipović and modulation spaces
Joachim Toft, Divyang G. Bhimani, Ramesh Manna
Abstract
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.
Topics & Concepts
PropagatorMathematicsHarmonic oscillatorModulation spaceFourier transformHarmonicMathematical analysisQuantum harmonic oscillatorHarmonic analysisPure mathematicsMathematical physicsQuantum mechanicsPhysicsMathematical Analysis and Transform MethodsAdvanced Harmonic Analysis ResearchAdvanced Mathematical Physics Problems