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Extension of CR functions to «wedge type» domains

Andrea D'Agnolo, Piero D'Ancona, Giuseppe Zampieri (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let X be a complex manifold, S a generic submanifold of X R , the real underlying manifold to X . Let Ω be an open subset of S with Ω analytic, Y a complexification of S . We first recall the notion of Ω -tuboid of X and of Y and then give a relation between; we then give the corresponding result in terms of microfunctions at the boundary. We relate the regularity at the boundary for ¯ b to the extendability of C R functions on Ω to Ω -tuboids of X . Next, if X has complex dimension 2, we give results on extension...

Fredholm spectrum and growth of cohomology groups

Jörg Eschmeier (2008)

Studia Mathematica

Let T ∈ L(E)ⁿ be a commuting tuple of bounded linear operators on a complex Banach space E and let σ F ( T ) = σ ( T ) σ e ( T ) be the non-essential spectrum of T. We show that, for each connected component M of the manifold R e g ( σ F ( T ) ) of all smooth points of σ F ( T ) , there is a number p ∈ 0, ..., n such that, for each point z ∈ M, the dimensions of the cohomology groups H p ( ( z - T ) k , E ) grow at least like the sequence ( k d ) k 1 with d = dim M.

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