General convolutions of integral transforms and their application to ode and PDE problems
Abstract
The present research is devoted to some polyconvolutions generated by various integral transforms. For example, we study convolutions of the Hankel transform with the following factorization properties:
where Hv[f] (x) is the Hankel transform. Conditions for the existence of the constructed polyconvolutions are found. The results of this research are applied for solvability of ODEs and PDEs by the method of integral transforms. The derived constructions allow us to solve various nonuniform equations.
First Published Online: 14 Oct 2010
Keywords:
integral transforms, convolutions, Hankel transform, ODE, PDEHow to Cite
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Copyright (c) 2006 The Author(s). Published by Vilnius Gediminas Technical University.
This work is licensed under a Creative Commons Attribution 4.0 International License.
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Copyright
Copyright (c) 2006 The Author(s). Published by Vilnius Gediminas Technical University.
License
This work is licensed under a Creative Commons Attribution 4.0 International License.