关于Orlicz空间中Durrmeyer-采样型算子的收敛性质
On the convergence properties of Durrmeyer-Sampling Type Operators in Orlicz spaces
AI总结：
本文统一研究了Durrmeyer采样型级数算子在Orlicz空间中的收敛性，给出逐点与一致收敛定理、逼近阶定量估计及模收敛定理，并推广到多种函数空间，辅以实例和图示。
摘要：
本文对一类一般形式的采样型算子的收敛性给出统一处理，该算子由所谓的Durrmeyer采样型级数给出。特别地，我们在$\mathbb{R}$上给出了逐点收敛和一致收敛定理，并在此背景下，利用被逼近函数的连续模，给出了逼近阶的定量估计。随后，我们在Orlicz空间$L^φ(\mathbb{R})$的一般框架下得到了模收敛定理。由后一结果，$L^p(\mathbb{R})$空间、$L^α\log^βL$空间以及指数空间中的收敛性可作为特例推出。最后，针对若干具有特殊核的采样级数，给出了应用和例子，并附有图形表示。
英文摘要：
Here we provide a unifying treatment of the convergence of a general form of sampling type operators, given by the so-called Durrmeyer sampling type series. In particular we provide a pointwise and uniform convergence theorem on $\mathbb{R}$, and in this context we also furnish a quantitative estimate for the order of approximation, using the modulus of continuity of the function to be approximated. Then we obtain a modular convergence theorem in the general setting of Orlicz spaces $L^φ(\mathbb{R})$. From the latter result, the convergence in $L^p(\mathbb{R})$-space, $L^α\log^βL$, and the exponential spaces follow as particular cases. Finally, applications and examples with graphical representations are given for several sampling series with special kernels.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
