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

2024/04/04 by Nguyen Thi Hong Phuong, Phuong, Nguyen Thi Hong, Vu Kim Tuan +3 · 1 citation
Mathematics · #26D10 #42A38 #44A05 #65R10 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2404.03609

openalex publication_date 2024/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Derived from the results in [Giang et al.: 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(-(1)/(2)y²) 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 L₁ 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.

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