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An ordinal version of some applications of the classical interpolation theorem

Benoît Bossard (1997)

Fundamenta Mathematicae

Let E be a Banach space with a separable dual. Zippin’s theorem asserts that E embeds in a Banach space E 1 with a shrinking basis, and W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński have shown that E is a quotient of a Banach space E 2 with a shrinking basis. These two results use the interpolation theorem established by W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński. Here, we prove that the Szlenk indices of E 1 and E 2 can be controlled by the Szlenk index of E, where the Szlenk index...

Analyses multi-résolutions non orthogonales, commutation entre projecteurs et derivation et ondelettes vecteurs à divergence nulle.

Pierre Gilles Lemarie-Rieusset (1992)

Revista Matemática Iberoamericana

The notion of non-orthogonal multi-resolution analysis and its compatibility with differentiation (as expressed by the commutation formula) lead us to the construction of a multi-resolution analysis of L2(Rn)n which is well adapted to the approximation of divergence-free vector functions. Thus, we obtain unconditional bases of compactly supported divergence-free vector wavelets.

Analytic cohomology of complete intersections in a Banach space

Imre Patyi (2004)

Annales de l’institut Fourier

Let X be a Banach space with a countable unconditional basis (e.g., X = ℓ 2 ), Ω ⊂ X an open set and f 1 , ... , f k complex-valued holomorphic functions on Ω , such that the Fréchet differentials d f 1 ( x ) , ... , d f k ( x ) are linearly independant over ℂ at each x ∈ Ω . We suppose that M = { x ∈ Ω : f 1 ( x ) = ... = f k ( x ) = 0 } is a complete intersection and we consider a holomorphic Banach vector bundle E → M . If I (resp. 𝒪 E ) denote the ideal of germs of holomorphic functions on Ω that vanish on M (resp. the sheaf of germs of holomorphic sections of E ), then the sheaf cohomology groups H q ( Ω , I ) , H q ( M , 𝒪 E ) vanish...

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