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Some questions of approximation and representation of functions

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Collected Works

Part of the book series: Vladimir I. Arnold - Collected Works ((ARNOLD,volume 1))

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Abstract

1. Statement of the problem. Let f and g be functions of two variables. Then

$$ F(x, y, z) = f[x, g (y, z)] $$

is a function of the three variables x, y and z. This is an example of a superposition constituted of the functions f and g.

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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of California, 94720-3840, Berkeley, CA, USA

    Alexander B. Givental

  2. Department of Mathematics, University of Toronto, M5S 3G3, Toronto, ON, Canada

    Boris A. Khesin

  3. Control & Dynamical Systems and Applied & Computational Mathematics, California Institute of Technology, 91125-8100, Pasadena, CA, USA

    Jerrold E. Marsden

  4. Department of Mathematics, University of North Carolina, 27599-3250, Chapel Hill, NC, USA

    Alexander N. Varchenko

  5. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, 119991, Moscow, Russian Federation

    Oleg Ya. Viro

  6. Institute of Mathematical Sciences, Stony Brook University, 11794-3660, Stony Brook, NY, USA

    Vladimir M. Zakalyukin

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(2009). Some questions of approximation and representation of functions. In: Givental, A., et al. Collected Works. Vladimir I. Arnold - Collected Works, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01742-1_7

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