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A free stochastic partial differential equation

Yoann Dabrowski (2014)

Annales de l'I.H.P. Probabilités et statistiques

We get stationary solutions of a free stochastic partial differential equation. As an application, we prove equality of non-microstate and microstate free entropy dimensions under a Lipschitz like condition on conjugate variables, assuming also the von Neumann algebra R ω embeddable. This includes an N -tuple of q -Gaussian random variables e.g. for | q | N ≤ 0 . 13 .

A full characterization of multipliers for the strong ρ -integral in the euclidean space

Lee Tuo-Yeong (2004)

Czechoslovak Mathematical Journal

We study a generalization of the classical Henstock-Kurzweil integral, known as the strong ρ -integral, introduced by Jarník and Kurzweil. Let ( 𝒮 ρ ( E ) , ∥ · ∥ ) be the space of all strongly ρ -integrable functions on a multidimensional compact interval E , equipped with the Alexiewicz norm ∥ · ∥ . We show that each element in the dual space of ( 𝒮 ρ ( E ) , ∥ · ∥ ) can be represented as a strong ρ -integral. Consequently, we prove that f g is strongly ρ -integrable on E for each strongly ρ -integrable function f if and only if g is almost everywhere...

A function space Cp(X) not linearly homeomorphic to Cp(X) × ℝ

Witold Marciszewski (1997)

Fundamenta Mathematicae

We construct two examples of infinite spaces X such that there is no continuous linear surjection from the space of continuous functions c p ( X ) onto c p ( X ) × ℝ . I n p a r t i c u l a r , cp(X) i s n o t l i n e a r l y h o m e o m o r p h i c t o cp(X) × ℝ . One of these examples is compact. This answers some questions of Arkhangel’skiĭ.

A functional calculus description of real interpolation spaces for sectorial operators

Markus Haase (2005)

Studia Mathematica

For a holomorphic function ψ defined on a sector we give a condition implying the identity ( X , ( A α ) ) θ , p = x ∈ X | t - θ R e α ψ ( t A ) ∈ L ⁎ p ( ( 0 , ∞ ) ; X ) where A is a sectorial operator on a Banach space X. This yields all common descriptions of the real interpolation spaces for sectorial operators and allows easy proofs of the moment inequalities and reiteration results for fractional powers.

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