Fonctions rationnelles et théorie de la réalisation: le cas hyper-analytique

Une généralisation de l'intégrale stochastique de Wick–Itô

“…qui n'est pas sans rappeler le produit de Cauchy-Kovalesvkaya utilisé pour définir des fonctions hyperholomorphes rationnelles ; voir [2].…”

Fonctions rationnelles et problème de Gleason associés à l'opérateur de Dirac

“…The analysis in these papers allowed us to define rational hyperholomorphic functions (see [4] and [5]), and can be adapted to the Dirac operator. Still, that analysis did not reduce to the case of the Dirac operator for functions which do not depend on the variable x 0 .…”

“…, A n sont des matrices dont les éléments sont dans Cl 0,n et qui sont de dimensions appropriées.Comme dans[4] nous avons les caractérisations d'une fonction rationnelle en termes de réalisation, de restriction à l'hyperplan x 1 = 0 et en termes d'espaces invariants :…”

On the Structure of the Taylor Series in Clifford and Quaternionic Analysis

“…Hyperholomorphic rational functions were defined and studied both in the quaternionic and in the Clifford algebra contexts in [3,6] and in [1,2] space of hyperholomorphic homogeneous polynomials of degree 1, and they play a crucial role in the development of these theories, since, taking symmetrized products of them, one obtains the respective bases of the spaces of hyperholomorphic homogeneous polynomials of degree k. These polynomials in turn give rise to the Taylor series of hyperholomorphic functions; see [9][10][11]. In [1][2][3]6], the Fueter variables were introduced using the solution of Gleason's problem in the context at hand.…”

“…In [1][2][3]6], the Fueter variables were introduced using the solution of Gleason's problem in the context at hand. For the original description of the Fueter variables, we refer the reader to [11, p. 81].…”