When is f(x_1, x_2, . . ., x_n)=u_1(x_1)+u_2(x_2)+ . . . +u_n(x_n)?

A. Klopotowski; M. G. Nadkarni; K. P. S. Bhaskara Rao

When is f(x_1, x_2, . . ., x_n)=u_1(x_1)+u_2(x_2)+ . . . +u_n(x_n)?

Functional Analysis 2007-05-23 v1 General Topology

Authors: A. Klopotowski , M. G. Nadkarni , K. P. S. Bhaskara Rao

Abstract

We discuss subsets $S$ of ${\mathbb{R}}^n$ such that every real valued function $f$ on $S$ is of the form {equation*} f(x_1,x_2,...,x_n) = u_1(x_1) + u_2(x_2) + ... + u_n(x_n), {equation*} and the related concepts and situations in analysis.

Keywords

sum of functions real valued functions subsets of R^n additive decomposition analysis

Cite

@article{arxiv.math/0312122,
  title  = {When is f(x_1, x_2, . . ., x_n)=u_1(x_1)+u_2(x_2)+ . . . +u_n(x_n)?},
  author = {A. Klopotowski and M. G. Nadkarni and K. P. S. Bhaskara Rao},
  journal= {arXiv preprint arXiv:math/0312122},
  year   = {2007}
}

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10 pages, no figures, no tables

When is f(x_1, x_2, . . ., x_n)=u_1(x_1)+u_2(x_2)+ . . . +u_n(x_n)?

Abstract

Keywords

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