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Integral combinations of Heavisides
Author(s) -
Kainen Paul C.,
Kůrková Věra,
Vogt Andrew
Publication year - 2010
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200710029
Subject(s) - heaviside step function , pointwise , mathematics , infinity , representation (politics) , function (biology) , pure mathematics , complex plane , mathematical analysis , weight function , plane (geometry) , geometry , evolutionary biology , politics , political science , law , biology
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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