Funzioni regolari nell'algebra di Cayley
Generalization of Fueter's result to
Fueter's result (see [6,8]) on inducing quaternionic regular functions from holomorphic functions of a complex variable is extended to Euclidean spaces . It is then proved to be consistent with M. Sce's generalization for being odd integers [6].
Generalized holomorphic functions and Clifford analysis.
Generalized Moisil-Théodoresco systems and Cauchy integral decompositions.
Generalized multidimensional Hilbert transforms in Clifford analysis.
Harmonic functions on classical rank one balls
In questo articolo studieremo le relazioni fra le funzioni armoniche nella palla iperbolica (sia essa reale, complessa o quaternionica), le funzione armoniche euclidee in questa palla, e le funzione pluriarmoniche sotto certe condizioni di crescita. In particolare, estenderemo al caso quaternionico risultati anteriori dell'autore (nel caso reale), e di A. Bonami, J. Bruna e S. Grellier (nel caso complesso).
Hermitean Cauchy integral decomposition of continuous functions on hypersurfaces.
Hurwitz analysis: basic concepts and connection with Clifford analysis
Hurwitz pairs and Clifford valued inner products
After an overview of Hurwitz pairs we are showing how to actually construct them and discussing whether, for a given representation, all Hurwitz pairs of the same type are equivalent. Finally modules over a Clifford algebra are considered with compatible inner products; the results being then aplied to Hurwitz pairs.
Hyperbolic Fourth-R Quadratic Equation and Holomorphic Fourth-R Polynomials
MSC 2010: 30C10, 32A30, 30G35The algebra R(1; j; j2; j3), j4 = ¡1 of the fourth-R numbers, or in other words the algebra of the double-complex numbers C(1; j) and the corresponding functions, were studied in the papers of S. Dimiev and al. (see [1], [2], [3], [4]). The hyperbolic fourth-R numbers form other similar to C(1; j) algebra with zero divisors. In this note the square roots of hyperbolic fourth-R numbers and hyperbolic complex numbers are found. The quadratic equation with hyperbolic fourth-R...
Hypercomplex algebras, hypercomplex analysis and conformal invariance
Hyper-holomorphic cells and Fredholm theory.
Infinite-dimensional bicomplex Hilbert spaces.
Integral repesentations and its applications in Clifford analysis.
Iteration of a quaternionic quadratic family.
Jump conditions for a metaharmonic double layer potential on rectifiable closed Jordan curves in ℝ²
This paper is concerned with jump conditions for the double layer potential associated with the two-dimensional Helmholtz equation for Hölder continuous boundary data on arbitrary rectifiable Jordan closed curves in ℝ².
Les algèbres de Krasner-Tate
Les algèbres de Krasner-Tate
Linear substitution for basic sets of polynomials in Clifford analysis
Logarithmic derivative of the Euler Γ function in Clifford analysis.
The logarithmic derivative of the Γ-function, namely the ψ-function, has numerous applications. We define analogous functions in a four dimensional space. We cut lattices and obtain Clifford-valued functions. These functions are holomorphic cliffordian and have similar properties as the ψ-function. These new functions show links between well-known constants: the Eurler gamma constant and some generalisations, ζR(2), ζR(3). We get also the Riemann zeta function and the Epstein zeta functions.