Inequalities and consequences of new convolutions for the fractional Fourier transform with Hermite weights

Anh, Pham Ky; Castro, L. P.; Thao, P. T.; Tuan, Nguyen Minh

doi:10.1063/1.4972598

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2022

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Cited by 4 publications

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“…The properties of the convolutions may also be very diverse up to the concrete definition of each convolution (cf. [1,2,7,10,15,23,24,25]). The integral operators which are associated with each one of the know convolutions may have also a very distinct nature (see, e.g., [3,4,5,6,8,9,11,12,13,14,21,22]).…”

Section: Introductionmentioning

confidence: 99%

New convolutions for an oscillatory integral operator on the half-line

Castro¹,

Silva²,

Tuan³

2018

AIP Conference Proceedings

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The main purpose of this work is to present three new convolutions for oscillatory integral operators defined on the positive half-line and in the framework of L 1 Lebesgue spaces. Therefore, such new functions introduced by the new convolutions will have factorization properties when considering the oscillatory integral operators under consideration. Moreover, some fundamental and operational properties of the mentioned integral operator are also studied in the first part of the paper.

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Section: Introductionmentioning

confidence: 99%

New convolutions for an oscillatory integral operator on the half-line

Castro¹,

Silva²,

Tuan³

2018

AIP Conference Proceedings

Self Cite

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A new convolution theorem associated with the linear canonical transform

Huo

2018

SIViP

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In this paper, we first introduce a new notion of canonical convolution operator, and show that it satisfies the commutative, associative, and distributive properties, which may be quite useful in signal processing. Moreover, it is proved that the generalized convolution theorem and generalized Young's inequality are also hold for the new canonical convolution operator associated with the LCT. Finally, we investigate the sufficient and necessary conditions for solving a class of convolution equations associated with the LCT.

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