论文标题
通过三角总和的指数类型的整个函数的近似
Approximation of entire functions of exponential type by trigonometric sums
论文作者
论文摘要
令$σ> 0 $。对于$ 1 \ le p \ le \ infty $，伯恩斯坦太空$ b^p_σ$是l^p（r）$中所有$ f \ f \ f $ f $ in limllimenllimenllimenlliment limited to $σ$的Banach空间；也就是说，$ f $的分销傅立叶变换在$ [ - σ，σ] $中支持。我们研究了有限的三角学总和\ [p_τ（x）=χ_τ（x）\ sum_ {| k | k | \leστ/π} c_ { $τ\ to \ infty $，\其中\ $χ_τ$表示$ [ - τ，τ] $的指示函数。
Let $σ>0$. For $1\le p\le \infty$, the Bernstein space $B^p_σ$ is a Banach space of all $f\in L^p(R)$ such that $f$ is bandlimited to $σ$; that is, the distributional Fourier transform of $f$ is supported in $[-σ, σ]$. We study the approximation of\ $f\in B^p_σ by finite trigonometric sums \[ P_τ(x)=χ_τ(x) \sum_{|k|\le στ/π}c_{k,τ} e^{i\fracπτk x } \] in $L^p$ norm on $R$ as\ $τ\to\infty$,\ where\ $χ_τ$ denotes the indicator function of $[-τ, τ]$.
