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The spectral theory of multiplication operators and the recurrence properties for nondifferentiable functions in the Zygmund class Λ a *
Author(s) -
Anderson J. M.,
Housworth E. A.,
Pitt L. D.
Publication year - 1992
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300006902
Subject(s) - mathematics , multiplication (music) , class (philosophy) , hausdorff space , hausdorff measure , pure mathematics , zero (linguistics) , set (abstract data type) , measure (data warehouse) , spectral theory , linear operators , discrete mathematics , algebra over a field , combinatorics , mathematical analysis , hausdorff dimension , hilbert space , artificial intelligence , computer science , linguistics , philosophy , database , bounded function , programming language
. 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∈ C 1 ( 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.