The main aim of this paper is to construct explicitly orthogonal bases for the spaces of k‐
homogeneous polynomial solutions of the Hodge–de Rham system in the Euclidean space …

The Fischer Decomposition for the H-action and Its Applications Page 1 The Fischer
Decomposition for the H-action and Its Applications Roman Lávicka Abstract. Recently the …

The classical Fischer decomposition of spinor‐valued polynomials is a key result on
solutions of the Dirac equation in the Euclidean space. As is well‐known, it can be …

Abstract Recently the Gelfand-Tsetlin construction of orthogonal bases has been explicitly
described for homogeneous polynomial solutions of the Hodge-de Rham systems in the …

Without any doubt, complex analysis belongs to the most important areas of mathematics.
From its beginnings, there have been several attempts to generalize this deep theory to …

The massless field equations for lower integer and half-integer values of spin in Minkowski
space are fundamental equations in mathematical physics. Their counterpart in Euclidean …

Massless field equations are fundamental in particle physics. In Clifford analysis, the
Euclidean version of these equations has been dealt with, but it is not clear, even in …

Selfdual 2–forms in dimension 4 and their Fischer decomposition Page 1 Selfdual 2–forms in
dimension 4 and their Fischer decomposition Fred Brackx ∗ , Hennie De Schepper ∗ , Lukáš …

As an analogue of the massless field equations in Euclidean space, we consider the so-
called generalized Cauchy–Riemann equations introduced by E. Stein and G. Weiss. In the …

Title: New Integral Formulae in Hypercomplex Analysis Author: Mgr. Martin Sikora
Department: Mathematical Institute of Charles University Supervisor: prof. RNDr. Vladimír …