Blaschke Condition
المؤلف:
Krantz, S. G
المصدر:
"The Blaschke Condition." §9.1.5 in Handbook of Complex Variables. Boston, MA: Birkhäuser
الجزء والصفحة:
...
27-11-2018
955
Blaschke Condition
If ![<span style=]()
{a_j} subset= D(0,1)" src="http://mathworld.wolfram.com/images/equations/BlaschkeCondition/Inline1.gif" style="height:20px; width:80px" /> (with possible repetitions) satisfies
where 
is the unit open disk, and no 
, then there is a bounded analytic function on 
which has zero set consisting precisely of the 
s, counted according to their multiplicities. More specifically, the infinite product
where 
is a Blaschke factor and 
is the complex conjugate, converges uniformly on compact subsets of 
to a bounded analytic function 
.
REFERENCES:
Krantz, S. G. "The Blaschke Condition." §9.1.5 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 118-119, 1999.
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