Exponential forms and path integrals for complex numbers in dimensions.
Exponentials Form a Basis of Discrete Holomorphic Functions on a Compact
We show that discrete exponentials form a basis of discrete holomorphic functions on a finite critical map. On a combinatorially convex set, the discrete polynomials form a basis as well.
Extension du théorème de Cauchy aux fonctions d’une variable complexe de la forme
Extension theorem for complex Clifford algebras-valued functions on fractal domains.
Finely differentiable monogenic functions
Since 1970’s B. Fuglede and others have been studying finely holomorhic functions, i.e., ‘holomorphic’ functions defined on the so-called fine domains which are not necessarily open in the usual sense. This note is a survey of finely monogenic functions which were introduced in (Lávička, R., A generalisation of monogenic functions to fine domains, preprint.) like a higher dimensional analogue of finely holomorphic functions.
Finely holomorphic functions and finely harmonic morphisms.
Fischer decompositions in Euclidean and Hermitean Clifford analysis
Euclidean Clifford analysis is a higher dimensional function theory studying so–called monogenic functions, i.e. null solutions of the rotation invariant, vector valued, first order Dirac operator . In the more recent branch Hermitean Clifford analysis, this rotational invariance has been broken by introducing a complex structure on Euclidean space and a corresponding second Dirac operator , leading to the system of equations expressing so-called Hermitean monogenicity. The invariance of this...
Fonctions analytiques dans certains corps values au sens de Krull
Fonctions analytiques sur certains corps valués au sens de Krull.
Fonctions Généralisées et Analyse Non Standard.
Fonctions presque holomorphes
Function theory for a Beltrami algebra.
Function theory in sectors
It is shown that there is a one-to-one correspondence between uniformly bounded holomorphic functions of n complex variables in sectors of ℂⁿ, and uniformly bounded functions of n+1 real variables in sectors of that are monogenic functions in the sense of Clifford analysis. The result is applied to the construction of functional calculi for n commuting operators, including the example of differentiation operators on a Lipschitz surface in .
Functions of a quaternion variable which are gradients of real-valued functions.
Fundamental solutions for Dirac-type operators
We consider the Dirac-type operators D + a, a is a paravector in the Clifford algebra. For this operator we state a Cauchy-Green formula in the spaces and . Further, we consider the Cauchy problem for this operator.
Funzioni regolari nell'algebra di Cayley
Généralisation et extension à l'espace du théorème des résidus de Cauchy
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.