Truncus (mathematics)

Template:Cleanup In mathematics, the Nevanlinna class is a class of functions defined on a region of the complex plane. Functions in the class have positive harmonic majorants and hence are also said to be of bounded type.

More formally, let $\Omega$ be a region. A function $f$ is said to be of bounded type on $\Omega$ if $f$ is analytic on $\Omega$ and ${\log }^{+}|f(z)|$ has a harmonic majorant on $\Omega$ (where ${\log }^{+}(x)=max\{0,\log (x)\}$).

The class of all such $f$ on $\Omega$ is commonly denoted $N(\Omega )$ and is sometimes called the Nevanlinna class for $\Omega$. The Nevanlinna class includes all the Hardy classes.

Theorem A sufficient condition for $f$ to be of bounded type on $\Omega$ is that $f=g/u$ where $u$ and $g$ are bounded and analytic on $\Omega$ with $0<|u|$. If $\Omega$ is simply connected the condition is also necessary.

See also

• De Branges space
• Rolf Nevanlinna

References

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