论文标题
具有广义集成的傅立叶分析
Fourier analysis with generalized integration
论文作者
论文摘要
我们通过使用Henstock-Kurzweil积分理论概括了经典的傅立叶变换操作员$ \ MATHCAL {F} _ {P} $。结果表明，操作员等于$ hk $ -Fourier变换$ \ Mathcal {l}^p $，$ 1 <p \ p \ leq 2 $。特别地，将此表示的理论范围提高到数值上近似于上述子空间上函数的傅立叶变换。此外，我们在比勒布斯格理论中更一般条件下显示了傅立叶变换函数$ \ mathcal {f} _ {p}（f）$的可不同性。
We generalize the classic Fourier transform operator $\mathcal{F}_{p}$ by using the Henstock-Kurzweil integral theory. It is shown that the operator equals the $HK$-Fourier transform on a dense subspace of $\mathcal{ L}^p$, $1<p\leq 2$. In particular, a theoretical scope of this representation is raised to approximate numerically the Fourier transform of functions on the mentioned subspace. Besides, we show differentiability of the Fourier transform function $\mathcal{F}_{p}(f)$ under more general conditions than in Lebesgue's theory.
