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2013•INTERNATIONAL JOURNAL ON Advances in Information Sciences and Service SciencesRequires access

Properties of Fractional Mellin Transform

Yonggong Peng -, Yixian Wang, Xiangwu Zuo, Li-Hua Gong

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Abstract

Mellin transform and Fourier transform are related mathematically. Some properties of Mellin transform and fractional Mellin transform are generalized. By referring to the Parseval theorem of Fourier transform, a similar version of Mellin transform is formulated. The scale invariance property of fractional Mellin transform is derived and an extension of fractional Mellin transform is introduced. The construction of the two dimensional reality preserving fractional Mellin transform is also introduced.

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What this paper is about

Mellin transform and Fourier transform are related mathematically. Some properties of Mellin transform and fractional Mellin transform are generalized. By referring to the Parseval theorem of Fourier transform, a similar version of Mellin transform is formulated. The scale invariance property of fractional Mellin transform is derived and an extension of fractional Mellin transform is introduced. The construction of the two dimensional reality preserving fractional Mellin transform is also introduced.

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Available abstract

Mellin transform and Fourier transform are related mathematically. Some properties of Mellin transform and fractional Mellin transform are generalized. By referring to the Parseval theorem of Fourier transform, a similar version of Mellin transform is formulated. The scale invariance property of fractional Mellin transform is derived and an extension of fractional Mellin transform is introduced. The construction of the two dimensional reality preserving fractional Mellin transform is also introduced.

Key concepts: Mellin transform, Mellin inversion theorem, Mathematics, Fractional Fourier transform, Mathematical analysis, Laplace transform, Fourier transform, Fourier analysis

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