拟巴拿赫代数与拟微分算子和广义亚代数算子的Wiener性质
Quasi-Banach algebras and Wiener properties for pseudodifferential and generalized metaplectic operators
摘要：
本文将Gröchenig和Rzeszotnik在[24]中关于伪微分算子的巴拿赫代数的结果推广到傅里叶积分算子的拟代数.也就是说，我们引入准巴拿赫代数的符号类的傅里叶积分算子，我们称之为广义亚代数算子，包括伪微分算子。这个术语源于傅里叶积分算子的维纳代数的开创性工作[11]，我们将其推广到我们的框架。这一理论在发展方程的研究中得到了应用，例如具有有界扰动的薛定谔方程的柯西问题，参见。[7]。
英文摘要：
We generalize the results for Banach algebras of pseudodifferential operators obtained by Gröchenig and Rzeszotnik in [24] to quasi-algebras of Fourier integral operators. Namely, we introduce quasi-Banach algebras of symbol classes for Fourier integral operators that we call generalized metaplectic operators, including pseudodifferential operators. This terminology stems from the pioneering work on Wiener algebras of Fourier integral operators [11], which we generalize to our framework. This theory finds applications in the study of evolution equations such as the Cauchy problem for the Schrödinger equation with bounded perturbations, cf. [7].
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