Some integral operators and their relation to multidimensional Fourier-Bessel transform on Lα2(ℝ+n) and applications. Issue 3 (4th March 2022)

• Record Type: Journal Article
• Authors: Selmi, Belgacem; Allagui, Mohamed Ali
• Is Part Of: Integral transforms and special functions. Volume 33:Issue 3(2022)
• Page Start: 176
• Page End: 190
• Publication Date: 2022-03-04
• Subjects: Boundedness of integral operator -- Hilbert space -- multidimensional Fourier-Bessel transform; 46E35; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2021.1925666
• Languages: English
• ISSNs: 1065-2469

Abstract

Abstract : In this paper, we prove some properties of a class of integral operators defined in L α 2 ( R + n ), and we characterize a relation between this class of operators and multidimensional Fourier-Bessel transform F α associated with the differential operator Δ α, 1 Δ α = ∑ i = 1 n ∂ 2 ∂ x i 2 + 2 α i + 1 x i ∂ ∂ x i, α i > − 1 2 . We also construct a class of integral operators which commute with multidimensional Fourier-Bessel transform F α .