arXiv subjects

Lai Tien Minh

Publications and source records attributed to Lai Tien Minh.

3 recordsLinked to original sources

arXiv2026

$\mathcal{O}_α$-transformation and its uncertainty principles

In this paper, we introduce a family of integral transforms, denoted by $\mathcal{O}_α$, and constructed via kernel fusion of the fractional Fourier transform (FRFT) with angle $α\notin π\mathbb{Z}$. We demonstrate that the $\mathcal{O}_α$-transformation constitutes a well-defined integral operator by establishing its basic operational properties. Besides, we survey various mathematical aspects of the uncertainty principles for the $\mathcal{O}_α$-transform, including Heisenberg's inequality, logarithmic uncertainty inequality, local uncertainty inequality, Hardy's inequality, Pitt's inequality, and Beurling-H{ö}rmander's theorem.

math.CA↗

arXiv2025

Fundamental inequalities for the iterated Fourier-cosine convolution with Gaussian weight and its application

Derived from the results in [Giang et al.: \emph{Convolutions for the Fourier transforms with geometric variables and applications}, Math. Nachr. 283(12) (2010), 1758--1770], in this paper, we devoted to studying the boundedness properties for the Fourier-cosine convolution weighted by a Gaussian function of the form $γ=\exp(-\frac{1}{2}y^2)$ via Young's type theorem and Saitoh's type inequality. New norm estimations in the weighted space are obtained, and the application of the corresponding class of convolutions in Fredholm's second kind of integral equation is discussed. The conditions for the solvability of this equation on the $L_1$ space are also found, along with the analysis of an illustrative numerical example, which exemplifies that the present object and method solve cases that are not under the conditions of previously known techniques.

math.CA↗

arXiv2024

Analog version of Hausdorff--Young's theorem for quadratic Fourier transforms and boundedness of oscillatory integral operator

The purpose of this paper is twofold. The first aim is based on Riesz--Thorin's interpolation theorem, we prove new Hausdorff--Young type inequalities for the Quadratic Fourier transforms in (Ann. Funct. Anal. 2014;5(1):10--23) and linear canonical transforms in (Mediterr. J. Math. 2018;15,13), which were introduced by Castro et al. The second aim is to investigate the boundedness of the oscillatory integral operator with polynomial phases, which is also presented in the last section of the article.

math.CA↗