Nearly Holomorphic Functions on Hermitian Symmetric Spaces.
A notion of negligible sets for polydiscs is introduced. Some properties of non-negligible sets are proved. These results are used to construct good and good inner functions on polydiscs.
The formal class of a germ of diffeomorphism is embeddable in a flow if is formally conjugated to the exponential of a germ of vector field. We prove that there are complex analytic unipotent germs of diffeomorphisms at () whose formal class is non-embeddable. The examples are inside a family in which the non-embeddability is of geometrical type. The proof relies on the properties of some linear functional operators that we obtain through the study of polynomial families of diffeomorphisms...
We consider -tuples of commuting operators on a Banach space with real spectra. The holomorphic functional calculus for is extended to algebras of ultra-differentiable functions on , depending on the growth of , , when . In the non-quasi-analytic case we use the usual Fourier transform, whereas for the quasi-analytic case we introduce a variant of the FBI transform, adapted to ultradifferentiable classes.
We prove that for a real analytic generic submanifold of whose Levi-form has constant rank, the tangential -system is non-solvable in degrees equal to the numbers of positive and negative Levi-eigenvalues. This was already proved in [1] in case the Levi-form is non-degenerate (with non-necessarily real analytic). We refer to our forthcoming paper [7] for more extensive proofs.
A classical result of Hardy and Littlewood states that if is in , 0 < p ≤ 2, of the unit disk of ℂ, then where is a positive constant depending only on p. In this paper, we provide an extension of this result to Hardy and weighted Bergman spaces in the unit ball of , and use this extension to study some related multiplier problems in .
We introduce the extended bicomplex plane 𝕋̅, its geometric model: the bicomplex Riemann sphere, and the bicomplex chordal metric that enables us to talk about convergence of sequences of bicomplex meromorphic functions. Hence the concept of normality of a family of bicomplex meromorphic functions on bicomplex domains emerges. Besides obtaining a normality criterion for such families, the bicomplex analog of the Montel theorem for meromorphic functions and the fundamental normality tests for families...
We prove some normality criteria for families of meromorphic mappings of a domain into ℂPⁿ under a condition on the inverse images of moving hypersurfaces.