A Blaschke product is a specific type of function in complex analysis that is defined as a product of terms related to the holomorphic function behavior on the unit disk. Specifically, a Blaschke product is constructed using zeros that lie inside the unit disk. It is a powerful tool in the study of operator theory and function theory on the unit disk. Formally, if \(\{a_n\}\) is a sequence of points inside the unit disk (i.e.
Articles by others on the same topic
For zeros in the unit disc satisfying , with occurrences at zero, a Blaschke product isFor and , the normalized factor satisfies . The product therefore converges locally uniformly; outside its prescribed zeros the logarithms of its tail factors converge absolutely, so it has no additional zeros. Every finite product has modulus at most one in the disc, and the limit does too. Since is pseudohyperbolic distance from to , its modulus can be estimated geometrically.