Microfunctions with values in a Clifford algebra 1
Möbius transformations and monogenic functional calculus.
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...
Nonlinear singular integral equations involving the Hilbert transform in Clifford analysis.
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...
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 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 annihilators of harmonic vector fields
On Boolean partial differential equations
On Clifford-type structures [Book]
On domains of monogenicity in Clifford analysis
On Fueter-Hurwitz regular mappings [Book]
On holomorphic vector bundles on Hopf manifolds with trivial pullback on the universal covering.
On hyper f-structures.
On limiting values of Cauchy type integral in a harmonic algebra with two-dimensional radical
We consider a certain analog of Cauchy type integral taking values in a three-dimensional harmonic algebra with two-dimensional radical. We establish sufficient conditions for an existence of limiting values of this integral on the curve of integration.
On operators and elementary functions in Clifford analysis.