On a decomposition of polynomials in several variables

Andrzej Schinzel

Journal de théorie des nombres de Bordeaux (2002)

  • Volume: 14, Issue: 2, page 647-666
  • ISSN: 1246-7405

Abstract

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One considers representation of a polynomial in several variables as the sum of values of univariate polynomials taken at linear combinations of the variables.

How to cite

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Schinzel, Andrzej. "On a decomposition of polynomials in several variables." Journal de théorie des nombres de Bordeaux 14.2 (2002): 647-666. <http://eudml.org/doc/248917>.

@article{Schinzel2002,
abstract = {One considers representation of a polynomial in several variables as the sum of values of univariate polynomials taken at linear combinations of the variables.},
author = {Schinzel, Andrzej},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {polynomial approximation},
language = {eng},
number = {2},
pages = {647-666},
publisher = {Université Bordeaux I},
title = {On a decomposition of polynomials in several variables},
url = {http://eudml.org/doc/248917},
volume = {14},
year = {2002},
}

TY - JOUR
AU - Schinzel, Andrzej
TI - On a decomposition of polynomials in several variables
JO - Journal de théorie des nombres de Bordeaux
PY - 2002
PB - Université Bordeaux I
VL - 14
IS - 2
SP - 647
EP - 666
AB - One considers representation of a polynomial in several variables as the sum of values of univariate polynomials taken at linear combinations of the variables.
LA - eng
KW - polynomial approximation
UR - http://eudml.org/doc/248917
ER -

References

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  1. [1] N. Alon, M.B. Nathanson, I. Ruzsa, The polynomial method and restricted sums of congruence classes. J. Number Theory56 (1996), 404-417. Zbl0861.11006MR1373563
  2. [2] P. Diaconis, M. Shahshahani, On nonlinear functions of linear combinations. SIAM J. Sci. Stat. Comput.5 (1984), 175-191. Zbl0538.41041MR731890
  3. [3] W.J. Ellison, A 'Waring's problem' for homogeneous forms. Proc. Cambridge Philos. Soc.65 (1969), 663-672. Zbl0209.34305MR237450
  4. [4] U. Helmke, Waring's problem for binary forms. J. Pure Appl. Algebra80 (1992), 29-45. Zbl0791.11020MR1167385
  5. [5] A. Iarrobino, Inverse system of a symbolic power II. The Waring problem for forms. J. Algebra174 (1995), 1091-1110. Zbl0842.11016MR1337187
  6. [6] B.F. Logan, L.A. Shepp, Optimal reconstruction of a function from its projections. Duke Math. J.42 (1975), 645-659. Zbl0343.41020MR397240
  7. [7] T. Mum, A treatise on the theory of determinants. Dover, 1960. MR114826
  8. [8] B. Reznick, Sums of powers of complex linear forms, unpublished manuscript of 1992. 

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