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  • 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.
  • 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. (en)
Title
  • Integral Combinations of Heavisides
  • Integral Combinations of Heavisides (en)
skos:prefLabel
  • Integral Combinations of Heavisides
  • Integral Combinations of Heavisides (en)
skos:notation
  • RIV/67985807:_____/10:00043643!RIV11-GA0-67985807
http://linked.open...avai/riv/aktivita
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  • P(GA201/05/0557), P(GA201/08/1744), Z(AV0Z10300504)
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  • 6
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  • 264259
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  • RIV/67985807:_____/10:00043643
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  • 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 (en)
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  • US - Spojené státy americké
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  • [541703DBC978]
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  • Mathematische Nachrichten
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  • 283
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  • Kůrková, Věra
  • Kainen, P. C.
  • Vogt, A.
http://linked.open...ain/vavai/riv/wos
  • 000278819600006
http://linked.open...n/vavai/riv/zamer
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  • 0025-584X
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