Index transforms with the square of Bessel functions
Semyon Yakubovich

TL;DR
This paper introduces new index transforms with Bessel function kernels, explores their mathematical properties in Lebesgue spaces, proves inversion theorems, and applies them to solve a third-order PDE involving the Laplacian.
Contribution
It presents novel index transforms with Bessel functions, analyzes their properties, and demonstrates their application to solving specific PDEs.
Findings
Transform boundedness and invertibility in Lebesgue spaces established
Inversion theorems proved for the new transforms
Application to initial value problem for a third-order PDE involving Laplacian
Abstract
New index transforms, involving the square of Bessel functions of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue spaces. Inversion theorems are proved. As an interesting application, a solution to the initial value problem for the third order partial differential equation, involving the Laplacian, is obtained.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicsadvanced mathematical theories · Differential Equations and Boundary Problems · Algebraic and Geometric Analysis
