Počet záznamů: 1  

Integral Combinations of Heavisides

  1. 1. 0043643 - UIVT-O 2011 RIV US eng J - Článek v odborném periodiku
    Kainen, P.C. - Kůrková, Věra - Vogt, A.
    Integral Combinations of Heavisides.
    Mathematische Nachrichten. Roč. 283, č. 6 (2010), s. 854-878 ISSN 0025-584X
    Grant CEP: GA ČR GA201/05/0557; GA ČR GA201/08/1744
    Výzkumný záměr: CEZ:AV0Z10300504
    Klíčová slova: feedforward neural network * perceptron * heaviside function * plane wave * integral formula * radon transform * Green’s function for iterated Laplacians * order of vanishing * function of controlled decay
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 0.653, rok: 2010

    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 representation is proved here by elementary techniques with separate arguments for even and odd d, and unifies and extends various results in the literature.
    Trvalý link: http://hdl.handle.net/11104/0136577