Nearly Holomorphic Functions on Hermitian Symmetric Spaces.
Negligible sets and good functions on polydiscs
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.
Neuere Ergebnisse in der komplexen Analysis.
Nevanlinna-Cartan theory over function fields and a Diophantine equation.
Nevanlinna-Pick interpolation for Schur-Agler class functions on domains with matrix polynomial defining function in .
New characterizations of Bergman spaces.
Nicht endlich erzeugte Primideale in Steinschen Algebren.
Non-attainable boundary values of H∞ functions.
Non-embeddability of general unipotent diffeomorphisms up to formal conjugacy
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...
Non-extendable holomorphic functions
Non-extendable holomorphic functions of bounded growth in Reinhardt domains
Nonfactorization theorems for Hardy and Bergman spaces on bounded symmetric domains
Non-holomorphic functional calculus for commuting operators with real spectrum
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.
Non-homogeneous directional equations: Slice solutions belonging to functions of bounded -index in the unit ball
For a given direction we study non-homogeneous directional linear higher-order equations whose all coefficients belong to a class of joint continuous functions which are holomorphic on intersection of all directional slices with a unit ball. Conditions are established providing boundedness of -index in the direction with a positive continuous function satisfying some behavior conditions in the unit ball. The provided conditions concern every solution belonging to the same class of functions...
Non-solvability of the tangential -systems
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.
Non-Vanishing of the Bergman Kernel Function at Boundary Points of Certain Domains in Cn .
Norm and Taylor coefficients estimates of holomorphic functions in balls
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 .
Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball.
Normal families of bicomplex meromorphic functions
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...
Normal families of holomorphic functions on infinite-dimensional spaces.