Monogenic functions on surfaces.
More on modified quaternionic analysis in R3.
Morera type problems in Clifford analysis.
The Pompeiu and the Morera problems have been studied in many contexts and generality. For example in different spaces, with different groups, locally, without an invariant measure, etc. The variations obtained exhibit the fascination of these problems.In this paper we present a new aspect: we study the case in which the functions have values over a Clifford Algebra. We show that in this context it is completely natural to consider the Morera problem and its variations. Specifically, we show the...
Multipliers and weighted ∂ operator estimates.
We study estimates for the solution of the equation du=f in one variable. The new ingredient is the use of holomorphic functions with precise growth restrictions in the construction of explicit solution to the equation.
Nevanlinna theory on the p-adic plane
Let 𝕂 be a complete and algebraically closed non-Archimedean valued field. Following ideas of Marc Krasner and Philippe Robba, we define K-meromorphic functions from 𝕂 to 𝕂. We show that the Nevanlinna theory for functions of a single complex variable may be extended to those functions (and consequently to meromorphic functions).
Nonarchimedean Harmonie Analysis and Analytic Functions.
Nonlinear Riemann Boundary Value Problems for a Nonlinear Elliptic System in the Plane.
Nonlinear singular integral equations involving the Hilbert transform in Clifford analysis.
Norm Equalities of Analytic Mappings into Hilbert Spaces.
Norm Equalities of Vector-Valued Analytic Functions.
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...
Normality Domains for Families of Holomorphic Maps.
Notes on a generalized -conjecture over function fields
Oka-analyticity of the essential spectrum
On 4-dimensional locally conformally flat almost Kähler manifolds
Using the fundamental notions of the quaternionic analysis we show that there are no 4-dimensional almost Kähler manifolds which are locally conformally flat with a metric of a special form.
On a class of vector-valued analytic functions
On a direct decomposition of the space .
On a generalization of Fueter's theorem.
On a noncommutative algebraic geometry
Several sets of quaternionic functions are described and studied with respect to hyperholomorphy, addition and (non-commutative) multiplication, on open sets of ℍ, then Hamilton 4-manifolds analogous to Riemann surfaces, for ℍ instead of ℂ, are defined, and so begin to describe a class of four-dimensional manifolds.
On a residue of complex functions in the three-dimensional Euclidean complex vector space.