| The Mehler Formula for the Generalized Clifford-Hermite Polynomials |
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| 引用本文： | F. BRACKX N. DE SCHEPPER K. I. KOU F. SOMMEN. The Mehler Formula for the Generalized Clifford-Hermite Polynomials[J]. 数学学报(英文版), 2007, 23(4): 697-704. DOI: 10.1007/s10114-005-0754-7 |
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| 作者姓名： | F. BRACKX N. DE SCHEPPER K. I. KOU F. SOMMEN |
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| 作者单位： | [1]Clifford Research Group, Ghent University, Department of Mathematical Analysis, Faculty of Engineering, Galglaan 2, B-9000 Gent, Belgium [2]University of Macau, Department of Mathematics, Faculty of Science and Technology, P. O. Box 3001, Macau [3]Clifford Research Group, Ghent University, Department of Mathematical Analysis, Faculty of Sciences, Galglaan 2, B-9000 Gent, Belgium |
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| 基金项目： | The work is supported by Research Grant of the University of Macau No. RG021/03-045/QT/FST |
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| 摘 要： | The Mehler formula for the Hermite polynomials allows for an integral representation of the one-dimensional Fractional Fourier transform. In this paper, we introduce a multi-dimensional Fractional Fourier transform in the framework of Clifford analysis. By showing that it coincides with the classical tensorial approach we are able to prove Mehler＇s formula for the generalized Clifford-Hermite polynomials of Clifford analysis.
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| 关 键 词： | 广义Clifford-Hermite多项式 Mehler公式 变分傅立叶变换 Clifford分析 |
| 修稿时间： | 2004-04-152005-01-04 |
The Mehler Formula for the Generalized Clifford–Hermite Polynomials |
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| F. Brackx,N. de Schepper,K. I. Kou,F. Sommen. The Mehler Formula for the Generalized Clifford–Hermite Polynomials[J]. Acta Mathematica Sinica(English Series), 2007, 23(4): 697-704. DOI: 10.1007/s10114-005-0754-7 |
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| Authors: | F. Brackx N. de Schepper K. I. Kou F. Sommen |
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| Affiliation: | (1) Clifford Research Group, Ghent University, Department of Mathematical Analysis, Faculty of Engineering, Galglaan 2, B-9000 Gent, Belgium;(2) University of Macau, Department of Mathematics, Faculty of Science and Technology, 3001, Macau;(3) Clifford Research Group, Ghent University, Department of Mathematical Analysis, Faculty of Sciences, Galglaan 2, B-9000 Gent, Belgium |
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| Abstract: | The Mehler formula for the Hermite polynomials allows for an integral representation of the one–dimensional Fractional Fourier transform. In this paper, we introduce a multi–dimensional Fractional Fourier transform in the framework of Clifford analysis. By showing that it coincides with the classical tensorial approach we are able to prove Mehler’s formula for the generalized Clifford–Hermite polynomials of Clifford analysis. The work is supported by Research Grant of the University of Macau No. RG021/03–045/QT/FST |
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| Keywords: | Clifford analysis Fractional Fourier transform. Hermite Dolvnomials |
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