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Common zero sets of equivalent singular inner functions

100%

Izuchi K.

Studia Mathematica

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2004

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tom 163

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nr 3

231-255

EN

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 ${|ψ_{μ₀}| < 1} ∩ {|ψ_{λ₀}| < 1} = ∅$, where $ψ_{μ}$ is the associated singular inner function of μ. Let $𝓩(μ) = ⋂_{ν;ν∼ μ} Z(ψ_{ν})$ be the common zeros of equivalent singular inner functions of $ψ_{μ}$. Then 𝓩(μ) ≠ ∅ and 𝓩(μ) ∩ 𝓩(λ) = ∅. It follows that μ ≪ λ if and only if 𝓩(μ) ⊂ 𝓩(λ). Hence 𝓩(μ) is the set in the maximal ideal space of $H^{∞}$ which relates naturally to the set of measures equivalent to μ. Some basic properties of 𝓩(μ) are given.

2

Common zero sets of equivalent singular inner functions II

100%

Izuchi K.

Studia Mathematica

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2007

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tom 180

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nr 2

133-142

EN

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.

3

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An L-subspace generated by a certain measure with countable spectrum

44%

Izuchi K.

Colloquium Mathematicum

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1981

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tom 44

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nr 2

327-332

4

The structure of L-ideals of measures algebras

32%

Izuchi K.

Studia Mathematica

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1976-1977

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tom 59

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nr 2

125-131

Ograniczanie wyników

3 Studia Mathematica

1 Colloquium Mathematicum

4 Izuchi K.

1 2007

1 2004

1 1981

1 1976

Common zero sets of equivalent singular inner functions

Common zero sets of equivalent singular inner functions II

An L-subspace generated by a certain measure with countable spectrum

The structure of L-ideals of measures algebras