# Grace–Walsh–Szegő theorem

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# Grace–Walsh–Szegő theorem

Grace–Walsh–Szegő theorem

In mathematics, the **Grace–Walsh–Szegő coincidence theorem**^{[1]}^{[2]} is a result named after John Hilton Grace, Joseph L. Walsh, and Gábor Szegő.

Statement

Suppose *ƒ*(*z*1, ..., *z**n*) is a polynomial with complex coefficients, and that it is

symmetric, i.e. invariant under permutations of the variables, and

multi-affine, i.e. affine in each variable separately.

`Let`

*A*be a circular region in the complex plane. If either*A*isconvexor the degree of*ƒ*is*n*, then for everythere existssuch that## References

[1]

Citation Linkdoi.org"A converse to the Grace–Walsh–Szegő theorem",

*Mathematical Proceedings of the Cambridge Philosophical Society*, August 2009, 147(02):447–453. doi:10.1017/S0305004109002424Sep 20, 2019, 10:20 PM

[2]

Citation Linkopenlibrary.orgJ. H. Grace, "The zeros of a polynomial",

*Proceedings of the Cambridge Philosophical Society*11 (1902), 352–357.Sep 20, 2019, 10:20 PM

[4]

Citation Linken.wikipedia.orgThe original version of this page is from Wikipedia, you can edit the page right here on Everipedia.Text is available under the Creative Commons Attribution-ShareAlike License.Additional terms may apply.See everipedia.org/everipedia-termsfor further details.Images/media credited individually (click the icon for details).

Sep 20, 2019, 10:20 PM