Applications of Infinite Sums and Products

Steven G. Krantz
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Steven G. Krantz: Washington University in St. Louis, Department of Mathematics

Chapter Chapter 9 in Handbook of Complex Variables, 1999, pp 117-122 from Springer

Abstract: Abstract First we need means for manipulating the zeros of a holomorphic function on the disc. What we want is an analogue for the disc of the factors (z — a) that are used when we study polynomials on ℂ. The necessary device is what are called the Blaschke factors: If a ∈ D(0, 1), then we define the Blaschke factor 9.1.1.1 $${{B}_{a}}(z) = \frac{{z - a}}{{1 - \bar{a}z}}.$$ Observe that we have seen these functions before in the guise of Möbius transformations (§§5.5.1, §§6.2.2).

Date: 1999
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DOI: 10.1007/978-1-4612-1588-2_9

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