Science Fair Project Encyclopedia
Hadamard three-circle theorem
In complex analysis, a branch of mathematics, the Hadamard three-circle theorem is a result about the behavior of holomorphic functions.
Let f(z) be a holomorphic function on the annulus
Let M(r) be the maximum of | f(z) | on the circle | z | = r. Then, logM(r) is a convex function of the logarithm log(r). Moreover, if f(z) is not of the form czλ for some constants λ and c, then logM(r) is strictly convex as a function of log(r).
The conclusion of the theorem can be restated as
for any three concentric circles of radii r1 < r2 < r3.
See also
Last updated: 06-05-2005 03:22:17
10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details