Laguerre多项式与Toeplitz型算子的波函数
Wavelets from Laguerre polynomials and Toeplitz-type operators
摘要：
我们研究了Toeplitz型算子关于特定的小波，其傅里叶变换与Laguerre多项式。一方面，这种选择的小波强调了这样一个事实，即这些运营商的小波子空间上的共享许多性质与经典的Toeplitz运营商的伯格曼空间。另一方面，它使研究poly-Bergman空间和Toeplitz算子从不同的角度对他们的作用。在复平面的上半平面上，这些算子在符号上仅依赖于垂直变量，它们酉等价于具有特定函数的乘法算子。由于这个功能是负责这些Toeplitz型运营商和他们的代数的许多有趣的功能，我们更详细地研究其行为。作为一个副产品，我们得到了一个有趣的观察真正的多解析Bergman空间的渐近行为。描述了Calderón-Toeplitz算子代数和泛函代数之间的同构，并讨论了它们的结果.
英文摘要：
We study Toeplitz-type operators with respect to specific wavelets whose Fourier transforms are related to Laguerre polynomials. On the one hand, this choice of wavelets underlines the fact that these operators acting on wavelet subspaces share many properties with the classical Toeplitz operators acting on the Bergman spaces. On the other hand, it enables to study poly-Bergman spaces and Toeplitz operators acting on them from a different perspective. Restricting to symbols depending only on vertical variable in the upper half-plane of the complex plane these operators are unitarily equivalent to a multiplication operator with a certain function. Since this function is responsible for many interesting features of these Toeplitz-type operators and their algebras, we investigate its behavior in more detail. As a by-product we obtain an interesting observation about the asymptotic behavior of true polyanalytic Bergman spaces. Isomorphisms between the Calderón-Toeplitz operator algebras and functional algebras are described and their consequences are discussed.
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