论文标题
Wiener Tauberian定理用于操作员和功能
A Wiener Tauberian theorem for operators and functions
论文作者
论文摘要
我们在量子谐波分析的框架中证明了维也纳的陶伯里亚定理的变体，即，对于绝对可集成的函数与跟踪类操作员或两个跟踪类操作员之间的卷积。我们的结果包括Wiener的Tauberian Theorem作为特殊情况。我们的陶伯里亚定理的应用与本地化操作员，Toeplitz运算符，Bargmann-Fock空间和量化方案之间的同构定理有关，对Shubin的PseudoDifterential Operator colculus和Born-Jordan量化产生了影响。基于本地化操作员与Tauberian定理之间的联系，我们注意到，在我们的环境中，皮特的Tauberian定理的类似物意味着Toeplitz Operators的紧凑性在Berezin变换方面结果。此外，我们将结果扩展到Toeplitz运算符上的结果到由短期傅立叶变换引起的其他繁殖Hilbert空间，称为Gabor空间。最后，我们建立了维纳尔的陶伯里亚定理的等效性，以及由于费尔南德斯和加尔比斯而导致的定位操作员的紧凑性的条件。
We prove variants of Wiener's Tauberian theorem in the framework of quantum harmonic analysis, i.e. for convolutions between an absolutely integrable function and a trace class operator, or of two trace class operators. Our results include Wiener's Tauberian theorem as a special case. Applications of our Tauberian theorems are related to localization operators, Toeplitz operators, isomorphism theorems between Bargmann-Fock spaces and quantization schemes with consequences for Shubin's pseudodifferential operator calculus and Born-Jordan quantization. Based on the links between localization operators and Tauberian theorems we note that the analogue of Pitt's Tauberian theorem in our setting implies compactness results for Toeplitz operators in terms of the Berezin transform. In addition, we extend the results on Toeplitz operators to other reproducing kernel Hilbert spaces induced by the short-time Fourier transform, known as Gabor spaces. Finally, we establish the equivalence of Wiener's Tauberian theorem and the condition in the characterization of compactness of localization operators due to Fernández and Galbis.
