论文标题
几乎到处融合了球状球体系列
Almost Everywhere Convergence of Prolate Spheroidal Series
论文作者
论文摘要
在本文中，我们表明，就pr酸球形波函数而言，$ l^p $ - 帕利 - 维也纳类型空间的功能扩展几乎在任何地方都以$ 1 <p <\ infty $汇聚，即使在$ l^p $ -Norm中可能不会收敛。因此，我们考虑了函数的经典paley-wiener空间$ pw_c^p \ subset l^p（\ Mathcal {r}）$的功能，其傅立叶变换在$ [ - c，c] $中支持傅立叶变换和像paley-wiener一样的空格$ b_ {α，c} $ [H}^α$在$ [0，c] $中支持。作为侧面产品，我们显示了投影操作员的连续性$ p_c^αf：= \ nathcal {h}^α（χ_{[0，C]} $ l^q（0，\ infty）$，$ 1 <p \ leq q <\ infty $。
In this paper, we show that the expansions of functions from $L^p$-Paley-Wiener type spaces in terms of the prolate spheroidal wave functions converge almost everywhere for $1<p<\infty$, even in the cases when they might not converge in $L^p$-norm. We thereby consider the classical Paley-Wiener spaces $PW_c^p\subset L^p(\mathcal{R})$ of functions whose Fourier transform is supported in $[-c,c]$ and Paley-Wiener like spaces $B_{α,c}^p\subset L^p(0,\infty)$ of functions whose Hankel transform $\mathcal{H}^α$ is supported in $[0,c]$.As a side product, we show the continuity of the projection operator $P_c^αf:=\mathcal{H}^α(χ_{[0,c]}\cdot \mathcal{H}^αf)$ from $L^p(0,\infty)$ to $L^q(0,\infty)$, $1<p\leq q<\infty$.
