Clifford-Hermite-monogenic operators

Brackx, Freddy, de Schepper, Nele, and Sommen, Frank. "Clifford-Hermite-monogenic operators." Czechoslovak Mathematical Journal 56.4 (2006): 1301-1322. <http://eudml.org/doc/31106>.

@article{Brackx2006,
abstract = {In this paper we consider operators acting on a subspace $\mathcal \{M\}$ of the space $L_2(\mathbb \{R\}^m;\mathbb \{C\}_m)$ of square integrable functions and, in particular, Clifford differential operators with polynomial coefficients. The subspace $\{\mathcal \{M\}\}$ is defined as the orthogonal sum of spaces $\{\mathcal \{M\}\}_\{s,k\}$ of specific Clifford basis functions of $L_2(\mathbb \{R\}^m;\mathbb \{C\}_m)$. Every Clifford endomorphism of $\{\mathcal \{M\}\}$ can be decomposed into the so-called Clifford-Hermite-monogenic operators. These Clifford-Hermite-monogenic operators are characterized in terms of commutation relations and they transform a space $\{\mathcal \{M\}\}_\{s,k\}$ into a similar space $\{\mathcal \{M\}\}_\{s^\{\prime \}\!,k^\{\prime \}\}$. Hence, once the Clifford-Hermite-monogenic decomposition of an operator is obtained, its action on the space $\{\mathcal \{M\}\}$ is known. Furthermore, the monogenic decomposition of some important Clifford differential operators with polynomial coefficients is studied in detail.},
author = {Brackx, Freddy, de Schepper, Nele, Sommen, Frank},
journal = {Czechoslovak Mathematical Journal},
keywords = {differential operators; Clifford analysis; differential operators; Clifford analysis},
language = {eng},
number = {4},
pages = {1301-1322},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Clifford-Hermite-monogenic operators},
url = {http://eudml.org/doc/31106},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Brackx, Freddy
AU - de Schepper, Nele
AU - Sommen, Frank
TI - Clifford-Hermite-monogenic operators
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 4
SP - 1301
EP - 1322
AB - In this paper we consider operators acting on a subspace $\mathcal {M}$ of the space $L_2(\mathbb {R}^m;\mathbb {C}_m)$ of square integrable functions and, in particular, Clifford differential operators with polynomial coefficients. The subspace ${\mathcal {M}}$ is defined as the orthogonal sum of spaces ${\mathcal {M}}_{s,k}$ of specific Clifford basis functions of $L_2(\mathbb {R}^m;\mathbb {C}_m)$. Every Clifford endomorphism of ${\mathcal {M}}$ can be decomposed into the so-called Clifford-Hermite-monogenic operators. These Clifford-Hermite-monogenic operators are characterized in terms of commutation relations and they transform a space ${\mathcal {M}}_{s,k}$ into a similar space ${\mathcal {M}}_{s^{\prime }\!,k^{\prime }}$. Hence, once the Clifford-Hermite-monogenic decomposition of an operator is obtained, its action on the space ${\mathcal {M}}$ is known. Furthermore, the monogenic decomposition of some important Clifford differential operators with polynomial coefficients is studied in detail.
LA - eng
KW - differential operators; Clifford analysis; differential operators; Clifford analysis
UR - http://eudml.org/doc/31106
ER -