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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

f(z)=z^mF(z)product_(j=1)^infty-(a^__j)/(|a_j|)B_(a_j)(z),

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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References

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. https://mathworld.wolfram.com/BlaschkeFactorization.html

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