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arXiv · 2009.03939

Approximation of entire functions of exponential type by trigonometric sums

Saulius Norvidas
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Abstract

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 $[-τ, τ]$.

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Saulius Norvidas. 2020-09-08. Approximation of entire functions of exponential type by trigonometric sums. https://arxiv.org/abs/2009.03939

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