Abstract:In this work we study the essential spectra of composition operators on weighted Bergman spaces of analytic functions which might be termed as "quasi-parabolic." This is the class of composition operators on A 2 α with symbols whose conjugate with the Cayley transform on the upper half-plane are of the form ϕ(z) = z + ψ(z), where ψ ∈ H ∞ (H) and ℑ(ψ(z)) > ǫ > 0. We especially examine the case where ψ is discontinuous at infinity. A new method is devised to show that this type of composition operators fall in a… Show more
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