The standard summation operator, the Euler-Maclaurin sum formula, and the Laplace transformation

Journal of the Australian Mathematical Society

John Boris Miller¹ 

关键词: primary 65 B 15;    44 A 10;    47 B 38;    secondary 47 B 38;    39 B 70;   

DOI  :  10.1017/S1446788700026148

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

A proof is given of the Euler-Maclaurin sum formula, on a Banach space of differentiable vector-valued functions of bounded exponential growth, using the Laplace transformation. Some related summation formulae are proved by the same methods. Properties of the standard summation operator are proved, namely spectral properties and boundedness, continuity and differentiability results.

【 授权许可】

Unknown