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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.

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