论文标题
Weyl-Heisenberg框架操作员和Kohn-Nirenberg符号
Weyl-Heisenberg frame operators and Kohn-Nirenberg symbols
论文作者
论文摘要
$ l^2（\ Mathbb {r}）$上的Weyl-Heisenberg框架操作员的Kohn-Nirenberg符号的明确表达式直接从来自新的窗口函数的Gabor原子中获得。这种仅使用基本傅立叶分析的新方法与分布理论无关，并且严格在$ l^2（\ mathbb {r}）$中起作用。在合适的情况下，引入了Kohn-Nirenberg操作员，并被证明是Weyl-Heisenberg框架操作员。
An explicit expression for the Kohn-Nirenberg symbol of a Weyl- Heisenberg frame operator on $L^2(\mathbb{R})$ is obtained directly from the Gabor atom coming from new classes of window functions. This new approach, using only elementary Fourier analysis, is independent of the theory of distributions and works strictly inside $L^2(\mathbb{R})$. Kohn-Nirenberg operators are introduced and are shown to be Weyl-Heisenberg frame operators in suitable cases.
