Blaschke Factorization

Let f be a bounded analytic function on D(0,1) vanishing to order m>=0 at 0 and let {a_j} be its other zeros, listed with multiplicities. Then


where F is a bounded analytic function on D(0,1), F is zerofree, z^_ is the complex conjugate, and

 sup_(z in D(0,1))|f(z)|=sup_(z in D(0,1))|F(z)|.

See also

Blaschke Factor

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Krantz, S. G. "Blaschke Factorization." §9.1.7 in Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 119, 1999.

Referenced on Wolfram|Alpha

Blaschke Factorization

Cite this as:

Weisstein, Eric W. "Blaschke Factorization." From MathWorld--A Wolfram Web Resource.

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