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| 1 | SPHERICAL MEANS, DISTRIBUTIONS AND CONVOLUTION OPERATORS IN CLIFFORD ANALYSIS显示文摘New higher dimensional distributions are introduced in the framework of Clifford analysis.They complete the picture already established in previous work, offering unity and structuralclarity. Amongst them are the building blocks of the principal value distribution, involvingspherical harmonics, considered by Horvath and Stein. | F.BRACKX R.DELANGHE F.SOMMEN | 2003 | Chinese Annals of Mathematics,Series B2003，24，2： | 5 |
| 2 | The Teodorescu Operator in Clifford Analysis显示文摘Euclidean Clifford analysis is a higher dimensional function theory centred around monogenic functions, i.e., null solutions to a first order vector valued rotation in-variant differential operator called the Dirac operator. More recently, Hermitian Clifford analysis has emerged as a new branch, offering yet a refinement of the Euclidean case; it focuses on the simultaneous null solutions, called Hermitian monogenic functions, to two Hermitian Dirac operators _z and _(zt) which are invariant under the action of the unitary group. In Euclidean Clifford analysis, the Teodorescu operator is the right inverse of the Dirac operator . In this paper, Teodorescu operators for the Hermitian Dirac operators _z and _(zt) are constructed. Moreover, the structure of the Euclidean and Hermitian Teodor-escu operators is revealed by analyzing the more subtle behaviour of their components. Finally, the obtained inversion relations are still refined for the differential operators is-suing from the Euclidean and Hermitian Dirac operators by splitting the Clifford algebra product into its dot and wedge parts. Their relationship with several complex variables theory is discussed. | F.BRACKX H.De SCHEPPER M.E. LUNA-ELIZARRARS M.SHAPIRO | 2012 | Chinese Annals of Mathematics,Series B2012，33，4： | 3 |
| 3 | The Mehler Formula for the Generalized Clifford-Hermite Polynomials显示文摘为 Hermite 多项式的 Mehler 公式允许一个维的部分 Fourier 变换的一个不可分的代表。在这篇论文,我们在克利福德分析的框架介绍 amulti 维的部分 Fourier 变换。由证明它与古典 tensorial 途径与一致,我们能为克利福德分析的概括 Clifford-Hermite 多项式证明 Mehler 的公式。 | F.BRACKX N.DE SCHEPPER K.I.KOU F.SOMMEN | 2007 | Acta Mathematica Sinica,English Series2007，23，4： | 1 |
| 4 | HILBERT-DIRAC OPERATORS IN CLIFFORD ANALYSIS显示文摘Around the central theme of 'square root' of the Laplace operator it is shown that the classical Riesz potentials of the first and of the second kind allow for an explicit expression of so-called Hilbert-Dirac convolution operators involving natural and complex powers of the Dirac operator. | F.BRACKX H.DE SCHEPPER | 2005 | Chinese Annals of Mathematics,Series B2005，26，1： | 1 |
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