Representations oe multivariate polynomials by sums op unlvarlate polynomlals in llnear porms

Colloquium Mathematicum

Volumn 112, Issue 2, 2008, Pages 201-233

  Bialynicki Birula, A ^a   Schinzel, A ^b  

^a UNIVERSITY OF WARSAW   (Poland)

^b INSTITUTE OF MATHEMATICS   (Poland)

Author keywords

Sums of powers of linear polynomials and forms; Waring problem

Indexed keywords

EID: 77953776386     PISSN: 00101354     EISSN: 17306302     Source Type: Journal    
DOI: 10.4064/cm112-2-2     Document Type: Article

References (15)

1. J. Alexander and A. Hirscliowitz, Polynomial interpolation in several variables, J. Algebraic Geom. 1 (1995), 201-222.
2. A. Clilebowicz and M. Wolowiec-Musial, Forms with a unique representation as sum of powers of linear forms, Tatra Mt. Math. Publ. 32 (2005), 33-39.
3. P. Comon and B. Maurrin, Decomposition of quantics in sums of powers of linear forms. Signal Processing 53(1996), 93-107.
4. W. J. Ellison, A “Waring’s problem” for homogeneous forms, Proc. Cambridge Philos. Soc. 65 (1969), 663-672.
5. D. K. Harrison, A Grothendieck ring of higher degree forms, J. Algebra 35 (1975), 623-638.
6. A. Iarrobino, Inverse system of a symbolic power II. The Waring problem for forms, J. Algebra 174 (1995), 1091-1110.
7. A. Iarrobino and V. Kanev, Power Sums, Gorenstein Algebras and Determinantal Loci, Lecture Notes in Math. 1721, Springer, 1999.
8. J. Kleppe, Representing a homogeneous polynomial as a sum of powers of linear forms, thesis for the degree of Candidatus Scientiarum, Department of Mathematics, Univ. of Oslo, 1999.
9. R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia Math. Appl. 20, Addison-Wesley, Reading, MA, 1983.
10. M. Mella, Singularities of linear systems and the Waring problem, Trans. Amer. Math. Soc. 358 (2006), 5523-5538.
11. L. Redei, Algebra, Erster Teil, Geest & Portig, Leipzig, 1959.
12. A. Schinzel, On a decomposition of polynomials in several variables, J. Theorie Nombres Bordeaux 14 (2002), 647-666.
13. A. Schinzel, On a decomposition of polynomials in several variables II, Colloq. Math. 92 (2002), 67-79.
14. I. R. Shafarevich, Basic Algebraic Geometry, I, translated from the 1988 Russian edition. Springer, Berlin, 1994.
15. M. Wołowiec-Musiał, Problem no 6, Tatra Mt. Math. Publ. 32 (2005), 144.