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Integral combinations of Heavisides

✍ Scribed by Paul C. Kainen; Věra Kůrková; Andrew Vogt

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
262 KB
Volume
283
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

A sufficiently smooth function of d variables that decays fast enough at infinity can be represented pointwise by an integral combination of Heaviside plane waves (i.e., characteristic functions of closed half‐spaces). The weight function in such a representation depends on the derivatives of the represented function. The represen‐tation is proved here by elementary techniques with separate arguments for even and odd d, and unifies and extends various results in the literature (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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