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Title: Inequalities and consequences of new convolutions for the fractional Fourier transform with Hermite weights
Author: Anh, P. K.
Castro, L. P.
Thao, P. T.
Tuan, N. M.
Keywords: Fractional Fourier transform
Hermite function
Young's convolution inequality
Integral equation
Issue Date: 27-Jan-2017
Publisher: American Institute of Physics
Abstract: This paper presents new convolutions for the fractional Fourier transform which are somehow associated with the Hermite functions. Consequent inequalities and properties are derived for these convolutions, among which we emphasize two new types of Young's convolution inequalities. The results guarantee a general framework where the present convolutions are well-defined, allowing larger possibilities than the known ones for other convolutions. Furthermore, we exemplify the use of our convolutions by providing explicit solutions of some classes of integral equations which appear in engineering problems.
Peer review: yes
DOI: 10.1063/1.4972598
ISSN: 1551-7616
Appears in Collections:CIDMA - Artigos
FAAG - Artigos

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