Grace–Walsh–Szegő theorem

542 VIEWS

Everipedia is now IQ.wiki - Join the IQ Brainlist and our Discord for early access to editing on the new platform and to participate in the beta testing.

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(z1, ..., 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/S0305004109002424

Sep 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

[3]

Citation Linkdoi.org10.1017/S0305004109002424

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