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The spectral theory of multiplication operators and the recurrence properties for nondifferentiable functions in the Zygmund class Λ*a
Published online by Cambridge University Press: 26 February 2010
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Abstract. Let Φ be in the disc algebra H∞ ∩ C(T) with its restriction to T in the Zygmund space of smooth functions λ*(T). If P(Φ') ⊂ T is the set of Plessner points of Φ' and if F = Φ + Ψ, where Ψ∈C1(T), it is shown that F(P(Φ')) ⊆ C is a set of zero linear Hausdorff measure. Applications are given to the spectral theory of multiplication operators.
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- Copyright © University College London 1992
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