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Abstract

Let K be a real function of a real variable such that K≥0, K is continuous,zero outside some bounded interval,and

$$\int_{{ - \infty }}^{\infty } {K\left( t \right)dt = 1}$$

Define \({{K}_{n}}(t) = nK(nt)\) Show that is a Dirac sequence.

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© 1998 Springer Science+Business Media New York

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Shakarchi, R. (1998). Approximation with Convolutions. In: Problems and Solutions for Undergraduate Analysis. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1738-1_12

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  • DOI: https://doi.org/10.1007/978-1-4612-1738-1_12

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-98235-9

  • Online ISBN: 978-1-4612-1738-1

  • eBook Packages: Springer Book Archive

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