Non-similarity of Walsh and trigonometric systems

P. Wojtaszczyk

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We characterize the UMD-property of a Banach space X by sequences of ideal norms associated with trigonometric orthonormal systems. The asymptotic behavior of those numerical parameters can be used to decide whether X is a UMD-space. Moreover, if this is not the case, we obtain a measure that shows how far X is from being a UMD-space. The main result is that all described sequences are not only simultaneously bounded but are also asymptotically equivalent.

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In this paper we have collected some partial results on the sign of u(t,x) where u is a (sufficiently regular) solution of ⎧ u_tt + (-1)^m Δ^mu = 0 (t,x) ∈ R x Ω ⎨ ⎩ u_|Γ = ... = Δ^m-1 u_|Γ = 0 t ∈ R. These results rely on the study of a sign of almost periodic functions of a special...

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