Composition structure of polyconvolution associated with index Kontorovich–Lebedev transform and Fourier integrals
Year: 2025
Type: article
Abstract: Using Kakichev's classical concept and extending Yakubovich–Britvina's approach (Results Math. 2009;55(1–2):175–197) and (Integr Transforms Special Funct. 2010;21(4):259–276) for setting up Kontorovich–Lebedev convolution operators, this paper proposes a new polyconvolution structure associated with the KL-transform and Fourier integrals. Our main contributions include demonstrating a one-dimensional Watson-type transform, providing necessary and sufficient conditions for this transform to serve as unitary on L2(R+), and inferring its inverse operator in symmetric form. The existence of this structure over specific function spaces and its connection with previously known convolutions are pointed out. Establish the Plancherel-type theorem, prove the convergence in the mean-square sense in L2(R+), and prove the boundedness of dual spaces via Riesz-Thorin's theorem. Derives new weighted Lp-norm inequalities and boundedness in a three-parametric family of Lebesgue spaces. These theoretical findings are applied to solve specific classes of the Toeplitz–Hankel equation, providing a priori estimations based on the established conditions for L1 solvability.
Author: Trinh Tuan
Institution: Electric Power University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4412509477