A biholomorphism from the Bell representative domain onto an annulus and kernel functions

Mustafa Ersin Deger, Purdue University


Let Aρ2,1 = { z ∈ C : ρ2 < :z: < 1} and let Ω r = {z ∈ C : :z + 1z : < r}. It is known that for r > 2, Ω r is a doubly-connected domain with an algebraic Bergman kernel and satisfies a certain quadrature identity. We find an explicit biholomorphism between these two domains, and get the value of ρ as a function of r, which follows from the computation of the biholomorphism. Using the transformation formula for the Bergman kernel, we write out the Bergman kernel of the Bell representative domain Ωr, which was earlier known to be algebraic. We also determine the Ahlfors maps of this generalized quadrature domain using the Ahlfors map of the annulus. ^




Steven R. Bell, Purdue University.

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