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Valiron’s Interpolation Formula and a Derivative Sampling Formula in the Mellin Setting Acquired via Polar-Analytic Functions
Computational Methods and Function Theory ( IF 0.6 ) Pub Date : 2020-08-11 , DOI: 10.1007/s40315-020-00341-w Carlo Bardaro , Paul L. Butzer , Ilaria Mantellini , Gerhard Schmeisser
中文翻译:
通过极解析函数获得的Mellin环境中的Valiron插值公式和微分采样公式
更新日期:2020-08-11
Computational Methods and Function Theory ( IF 0.6 ) Pub Date : 2020-08-11 , DOI: 10.1007/s40315-020-00341-w Carlo Bardaro , Paul L. Butzer , Ilaria Mantellini , Gerhard Schmeisser
In this paper, we first recall some recent results on polar-analytic functions. Then we establish Mellin analogues of a classical interpolation of Valiron and of a derivative sampling formula. As consequences a new differentiation formula and an identity theorem in Mellin–Bernstein spaces are obtained. The main tool in the proofs is a residue theorem for polar-analytic functions.
中文翻译:
通过极解析函数获得的Mellin环境中的Valiron插值公式和微分采样公式
在本文中,我们首先回顾一下极分析函数的一些最新结果。然后,我们建立了Valiron经典插值法和衍生采样公式的Mellin类似物。结果,在Mellin-Bernstein空间中获得了新的微分公式和恒等式定理。证明中的主要工具是极坐标分析函数的残差定理。