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A Primer on the Dirichlet Space by Thomas Ransford, Javad Mashreghi, Karim Kellay, Omar El-Fallah

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6

Conformal invariance

Back in §1.4, we saw that if ϕ is a Möbius automorphism of the unit disk, then image for all fimage. Despite its simplicity, this observation has already proved useful, notably in the proof of Theorem 4.1.3. In this chapter, we start by showing that this Möbius-invariance property essentially characterizes the Dirichlet space. We then go on to study the problem of determining which other maps image leave invariant in the sense that This ...

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