Index transforms with the squares of Kelvin functions
Semyon Yakubovich
TL;DR
This paper introduces new index transforms based on squares of Kelvin functions, analyzes their properties, and applies them to solve a boundary value problem for a fourth order PDE on a wedge.
Contribution
It develops novel index transforms involving Kelvin functions and establishes their properties and inversion formulas, extending the mathematical toolkit for PDE boundary problems.
Findings
Mapping properties and inversion formulas in Lebesgue spaces
Application to a boundary value problem on a wedge
Solution of a fourth order PDE using the new transforms
Abstract
New index transforms, involving squares of Kelvin functions, are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The results are applied to solve a boundary value problem on the wedge for a fourth order partial differential equation.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Digital Filter Design and Implementation · Mathematical Analysis and Transform Methods