论文标题
k结构的傅立叶变换
k-Deformed Fourier Transform
论文作者
论文摘要
我们在$κ$笼统的统计力学框架中得出的$κ$ - 代数的图片中提出了一种新的傅立叶变换。 $κ$ -Fourier转换是从US [2013 Entropy {\ bf15} 624]最近推出的$κ$ -Fourier系列获得的。这种转换的内核将在$κ\ to0 $限制中降低到通常的指数阶段，由$κ$变形的相位和阻尼因子组成，并具有类似小波的行为的阻尼因子。我们表明，$κ$ -Fourier转换是通过更改时间和频率变量的标准傅立叶变换的异构。然而，根据傅立叶分析，新的形式主义对于研究$κ$ - 代理领域中定义的这些功能很有用。作为一个相关应用程序，我们讨论了$ n $ n $ aterate在统计上独立的随机变量的$κ$ sum的中心限制定理。
We present a new formulation of Fourier transform in the picture of the $κ$-algebra derived in the framework of the $κ$-generalized statistical mechanics. The $κ$-Fourier transform is obtained from a $κ$-Fourier series recently introduced by us [2013 Entropy {\bf15} 624]. The kernel of this transform, that reduces to the usual exponential phase in the $κ\to0$ limit, is composed by a $κ$-deformed phase and a damping factor that gives a wavelet-like behavior. We show that the $κ$-Fourier transform is isomorph to the standard Fourier transform through a changing of time and frequency variables. Nevertheless, the new formalism is useful to study, according to Fourier analysis, those functions defined in the realm of the $κ$-algebra. As a relevant application, we discuss the central limit theorem for the $κ$-sum of $n$-iterate statistically independent random variables.
