论文标题
分数空间中的傅立叶系列
Fourier Series in Fractional Dimensional Space
论文作者
论文摘要
在本文中，为任意定期函数$ f（t;α）$引入了分数维空间中的傅立叶序列。我们称其为“订单$α$”的分数傅立叶系列。通过旋转转换，将线性空间的基础函数扩展到分数一个，我们定义了一个真实而复杂的傅立叶序列并获得其系数。还表明，可以通过（分数）傅立叶序列实现定期函数的分数衍生物，并具有修改的系数。
In this paper, a Fourier series in fractional dimensional space is introduced for an arbitrarily periodic function $f(t;α)$. We call it fractional Fourier series of the order $α$. Extending the basis functions of the linear space into fractional one, by rotation transformation, we define a real and complex Fourier series and obtain their coefficients. It is also shown that the fractional derivative of a periodic function can be realized through (fractional) Fourier series with modified coefficients.
