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Fractional Clifford-Fourier transform and its application. (English) Zbl 1451.30098

Summary: In this paper, we consider a version of the fractional Clifford-Fourier transform (FrCFT) and study its several properties and applications to partial differential equations in Clifford analysis. First, we give the definition of the FrCFT and its inverse transform in the form of integral. Then, we discuss the relationship between the FrCFT and the Clifford-Fourier transform (CFT) and give some properties of the FrCFT, including Plancherel identity, differential properties, etc. Especially we give a new form of differential formula. Finally, we give an application of these results to a partial differential equation.

MSC:

30G35 Functions of hypercomplex variables and generalized variables
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
30E25 Boundary value problems in the complex plane
45E05 Integral equations with kernels of Cauchy type
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