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2017

Polynomial Norms

Ahmadi, Amir Ali, de Klerk, Etienne, Hall, Georgina

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In this paper, we study polynomial norms, i.e.

norms that are the $d^{\text{th}}$ root of a degree-$d$ homogeneous polynomial $f$.
We first show that a necessary and sufficient condition for $f^{1/d}$ to be a norm is for $f$ to be strictly convex, or equivalently, convex and positive definite.
Though not all norms come from $d^{\text{th}}$ roots of polynomials, we prove that any norm can be approximated arbitrarily well by a polynomial norm.

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E. Artin,
1927
Earlier work this paper cites.
W. W. Rogosinski,
1958
Earlier work this paper cites.
T. S. Motzkin,
1967
Earlier work this paper cites.
V. I. Dmitriev,
1973
Earlier work this paper cites.
D. Gondard and P. Ribenroim,
1974
Earlier work this paper cites.
C. Procesi and M. Schaher,
1976
Earlier work this paper cites.
M. R. Garey and D. S. Johnson,
1979
Earlier work this paper cites.
B. Reznick,
1979
Earlier work this paper cites.
L. Vandenberghe and S. Boyd,
1996
Earlier work this paper cites.
V. D. Blondel and J. N. Tsitsiklis,
2000
Earlier work this paper cites.
P. A. Parrilo,
2000
Earlier work this paper cites.
J. B. Lasserre,
2001
Earlier work this paper cites.
A. Shapiro,
2001
Earlier work this paper cites.

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