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

Published online by Cambridge University Press:  09 April 2009

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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1985

References

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