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Title: New convolutions for quadratic-phase Fourier integral operators and their applications
Author: Castro, L. P.
Minh, L. T.
Tuan, N. M.
Keywords: Convolution
Young inequality
Oscillatory integral
Convolution integral equation
Fractional Fourier transform
Linear canonical transform
Issue Date: 2-Jan-2018
Publisher: Springer
Abstract: We obtain new convolutions for quadratic-phase Fourier integral operators (which include, as subcases, e.g., the fractional Fourier transform and the linear canonical transform). The structure of these convolutions is based on properties of the mentioned integral operators and takes profit of weight-functions associated with some amplitude and Gaussian functions. Therefore, the fundamental properties of that quadratic-phase Fourier integral operators are also studied (including a Riemann-Lebesgue type lemma, invertibility results, a Plancherel type theorem and a Parseval type identity). As applications, we obtain new Young type inequalities, the asymptotic behaviour of some oscillatory integrals, and the solvability of convolution integral equations.
Peer review: yes
DOI: 10.1007/s00009-017-1063-y
ISSN: 1660-5446
Appears in Collections:CIDMA - Artigos
DMat - Artigos
FAAG - Artigos

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