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Conical Fourier-Borel transformations for harmonic functionals on the Lie ball

Mitsuo Morimoto, Keiko Fujita (1996)

Banach Center Publications

Let L(z) be the Lie norm on ˜ = n + 1 and L*(z) the dual Lie norm. We denote by Δ ( B ˜ ( R ) ) the space of complex harmonic functions on the open Lie ball B ˜ ( R ) and by E x p Δ ( ˜ ; ( A , L * ) ) the space of entire harmonic functions of exponential type (A,L*). A continuous linear functional on these spaces will be called a harmonic functional or an entire harmonic functional. We shall study the conical Fourier-Borel transformations on the spaces of harmonic functionals or entire harmonic functionals.

Corrigendum to: Holomorphic Morse inequalities on manifolds with boundary

Robert Berman (2008)

Annales de l’institut Fourier

A statement in the paper “Holomorphic Morse inequalities on manifolds with boundary” saying that the holomorphic Morse inequalities for an hermitian line bundle L over X are sharp as long as L extends as semi-positive bundle over a Stein-filling is corrected, by adding certain assumptions. A more general situation is also treated.

Diagonal series of rational functions

Sławomir Cynk, Piotr Tworzewski (1991)

Annales Polonici Mathematici

Some representations of Nash functions on continua in ℂ as integrals of rational functions of two complex variables are presented. As a simple consequence we get close relations between Nash functions and diagonal series of rational functions.

Estimates for the Bergman and Szegö projections for pseudoconvex domains of finite type with locally diagonalizable Levi form.

Philippe Charpentier, Yves Dupain (2006)

Publicacions Matemàtiques

In this paper, we give precise isotropic and non-isotropic estimates for the Bergman and Szegö projections of a bounded pseudoconvex domain whose boundary points are all of finite type and with locally diagonalizable Levi form. Additional local results on estimates of invariant metrics are also given.

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