带Hermite函数的Banach Gabor框架：Heisenberg群上的多解析空间
Banach Gabor frames with Hermite functions: polyanalytic spaces from the Heisenberg group
摘要：
具有Hermite函数的Gabor框架等价于多解析函数的真Fock空间中的采样序列。在L^2-情况下，这样的等价性来自多解析巴格曼变换的酉性。我们将介绍多解析函数的巴拿赫空间，并研究多解析Bargmann变换在调制空间上的映射性质。将共轨空间和定域标架理论应用于Heisenberg群的Fock表示，得到了显式的多解析抽样定理，它可以看作是J.M. Whittaker在他的书“插值函数理论”的第5章中。
英文摘要：
Gabor frames with Hermite functions are equivalent to sampling sequences in true Fock spaces of polyanalytic functions. In the L^2-case, such an equivalence follows from the unitarity of the polyanalytic Bargmann transform. We will introduce Banach spaces of polyanalytic functions and investigate the mapping properties of the polyanalytic Bargmann transform on modulation spaces. By applying the theory of coorbit spaces and localized frames to the Fock representation of the Heisenberg group, we derive explicit polyanalytic sampling theorems which can be seen as a polyanalytic version of the lattice sampling theorem discussed by J. M. Whittaker in Chapter 5 of his book "Interpolatory Function Theory".
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
