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

Part of: Acceleration of convergence Special classes of linear operators

Published online by Cambridge University Press:  09 April 2009

John Boris Miller
John Boris Miller
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia
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Abstract

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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.

Keywords

standard summation operatorEuler-Maclaurin formulaLaplace transformationfunctions of exponential growthdifferentiation operatorintegration operatorBernoulli polynomialsperiodic extensionperiodic Bernoulli polynomialsfunctional equation

MSC classification

Secondary: 65B15: Euler-Maclaurin formula 47B38: Operators on function spaces (general)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 3 , December 1985 , pp. 367 - 390
Copyright
Copyright © Australian Mathematical Society 1985

References

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