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Real Paley-Wiener theorems for the clifford fourier transform

Science China Mathematics 2014年第11期57卷 2381-2392页

作者： FU YingXiong LI LuoQing School of Mathematics and Statistics Hubei University

Associated with the Dirac operator and partial derivatives,this paper establishes some real PaleyWiener type theorems to characterize the clifford-valued functions whose clifford fourier transform(CFT) has compact support. Based on the Riemann-Lebesgue theorem for the CFT,the Boas theorem is provided to describe the CFT of clifford-valued functions that vanish on a neighborhood of the origin.

关键词： clifford fourier transform Dirac operator Paley-Wiener theorem Boas theorem

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Real clifford Windowed fourier transform

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Acta Mathematica Sinica,English Series 2011年第3期27卷 505-518页

作者： Mawardi BAHRI Sriwulan ADJI Ji Man ZHAO Department of Mathematics Hasanuddin University Tamalanrea Makassar 90245 Indonesia School of Mathematical Sciences Universiti Sains Malaysia 11800 Penang Malaysia School of Mathematical Sciences Key Laboratory of Mathematics and Complex Systems Beijing Normal University Beijing 100875 P. R. China

We study the windowed fourier transform in the framework of clifford analysis, which we call the clifford windowed fourier transform （CWFT）. Based on the spectral representation of the clifford fourier transform （CFT）, we derive several important properties such as shift, modulation, reconstruction formula, orthogonality relation, isometry, and reproducing kernel. We also present an example to show the differences between the classical windowed fourier transform （WFT） and the CWFT. Finally, as an application we establish a Heisenberg type uncertainty principle for the CWFT.

关键词： Multivector-valued function clifford analysis clifford fourier transform uncertainty principle

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Some Generalized clifford-Jacobi Polynomials and Associated Spheroidal Wavelets

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Analysis in Theory and Applications 2022年第4期38卷 394-416页

作者： Sabrine Arfaoui Anouar Ben Mabrouk Algebra Number Theory and Nonlinear Analysis Laboratory LR18ES15Department of MathematicsFaculty of SciencesMonastir 5000Tunisia Department of Mathematics Higher Institute of Applied Mathematics and Computer ScienceStreet of Assad Ibn AlfouratKairouan University3100 Kairouan Tunisia Department of Mathematics Faculty of SciencesUniversity of TabukSaudi Arabia

In the present paper,by extending some fractional calculus to the framework of clifford analysis,new classes of wavelet functions are ***,some classes of monogenic polynomials are provided based on 2-parameters weight functions which extend the classical Jacobi ones in the context of clifford *** discovered polynomial sets are next applied to introduce new wavelet *** formula as well as fourier-Plancherel rules have been *** main tool reposes on the extension of fractional derivatives,fractional integrals and fractional fourier transforms to clifford analysis.

关键词： Continuous wavelet transform clifford analysis clifford fourier transform fourier-plancherel fractional fourier transform fractional derivatives fractional integrals fractional clifford fourier transform Monogenic functions.

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