Pilipovic 空间与调制空间上的分数阶傅里叶变换、谐振子传播子及 Strichartz 估计
泛函分析
2023-03-16 v5
摘要
我们证明谐振子传播子与分数阶傅里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性质与固定时间估计，并将结果应用于证明谐振子传播子在调制空间上作用时的 Strichartz 估计。特别地，我们推广了 Balhara、Cordero、Nicola、Rodino 和 Thangavelu 的某些结果。我们还证明了分数阶谐振子传播子的一般形式在适当的 Pilipovic 空间上是连续的。
引用
@article{arxiv.2111.09575,
title = {Fractional Fourier transforms, harmonic oscillator propagators and Strichartz estimates on Pilipovic and modulation spaces},
author = {Joachim Toft and Divyang Bhimani and Ramesh Manna},
journal= {arXiv preprint arXiv:2111.09575},
year = {2023}
}
备注
38 pages. From version 4 to 5: Improvement of fractional powers of harmonic oscillator and their propagators on Hilbert spaces. From version 3 to 4: Several changes have been performed. Especially we have generalized some results to include multiple ordered fractional Fourier transforms and harmonic oscillator propagators. More references to literature, especially quantum theory and optics