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The spectral theory of multiplication operators and the recurrence properties for nondifferentiable functions in the Zygmund class Λ*a

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  26 February 2010

J. M. Anderson ,
E. A. Housworth  and
L. D. Pitt
J. M. Anderson
Affiliation:
Department of Mathematics, University College London, London. WC1E 6BT
E. A. Housworth
Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, Virginia, U.S.A.
L. D. Pitt
Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, Virginia, U.S.A.
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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.

MSC classification

Secondary: 30D40: Cluster sets, prime ends, boundary behavior

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Type
Research Article
Information
Mathematika , Volume 39 , Issue 1 , June 1992 , pp. 136 - 151
Copyright
Copyright © University College London 1992

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