2011/01/24 by Fred Brackx, Brackx, F., Hennie De Schepper +5 · 1 citation
Mathematics · #30G35 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.1101.4516
openalex publication_date 2011/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Hermitean Clifford analysis is a higher dimensional function theory centered around the simultaneous null solutions, called Hermitean monogenic functions, of two Hermitean conjugate complex Dirac operators. As an essential step towards the construction of an orthogonal basis of Hermitean monogenic polynomials, in this paper a Cauchy-Kovalevskaya extension theorem is established for such polynomials. The minimal number of initial polynomials needed to obtain a unique Hermitean monogenic extension is determined, along with the compatibility conditions they have to satisfy. The Cauchy-Kovalevskaya extension principle then allows for a dimensional analysis of the spaces of spherical Hermitean monogenics, i.e. homogeneous Hermitean monogenic polynomials. A version of this extension theorem for specific real-analytic functions is also obtained.