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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
Abstract
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.
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- 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
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