论文标题
与ITô-二级傅立叶变换的二元组合 - 热矿多项式
Dual of 2D fractional Fourier transform associated to Itô--Hermite polynomials
论文作者
论文摘要
在平面高斯希尔伯特（Gaussian Hilbert）空间上具有一类积分变换，在双盘上具有加权伯格曼空间的范围，被定义为与Itô-甲极地多种元素的Mehler函数相关的2D分数傅立叶变换的双变换。研究了这些变换的某些光谱特性。也就是说，我们研究了它们的界限，并确定其空空间及其范围。这样的识别取决于iTô-热线多项式的零。此外，给出了其奇异值的明确表达，并研究了P-Schatten类中的紧凑性和成员身份。还建立了与特定分数Hankel变换的关系
A class of integral transforms, on the planar Gaussian Hilbert space with range in the weighted Bergman space on the bi-disk, is defined as the dual transforms of the 2d fractional Fourier transform associated with the Mehler function for Itô--Hermite polynomials. Some spectral properties of these transforms are investigated. Namely, we study their boundedness and identify their null spaces as well as their ranges. Such identification depends on the zeros set of Itô--Hermite polynomials. Moreover, the explicit expressions of their singular values are given and compactness and membership in p-Schatten class are studied. The relationship to specific fractional Hankel transforms is also established
