Integral Combinations of Heavisides

0043643 - ÚI 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. E-ISSN 1522-2616
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