-type quotient modules on the torus.
Sidon sets and Fourier-Stieltjes transforms of some prime L-ideals.
An L-subspace generated by a certain measure with countable spectrum
The structure of L-ideals of measures algebras
Common zero sets of equivalent singular inner functions II
We study connected components of a common zero set of equivalent singular inner functions in the maximal ideal space of the Banach algebra of bounded analytic functions on the open unit disk. To study topological properties of zero sets of inner functions, we give a new type of factorization theorem for inner functions.
Common zero sets of equivalent singular inner functions
Let μ and λ be bounded positive singular measures on the unit circle such that μ ⊥ λ. It is proved that there exist positive measures μ₀ and λ₀ such that μ₀ ∼ μ, λ₀ ∼ λ, and , where is the associated singular inner function of μ. Let be the common zeros of equivalent singular inner functions of . Then (μ) ≠ ∅ and (μ) ∩ (λ) = ∅. It follows that μ ≪ λ if and only if (μ) ⊂ (λ). Hence (μ) is the set in the maximal ideal space of which relates naturally to the set of measures equivalent to μ....
Outer and inner vanishing measures and division in H + C.
Measures on the unit circle are well studied from the view of Fourier analysis. In this paper, we investigate measures from the view of Poisson integrals and of divisibility of singular inner functions in H + C. Especially, we study singular measures which have outer and inner vanishing measures. It is given two decompositions of a singular positive measure. As applications, it is studied division theorems in H + C.
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