Abstract
New index transforms are investigated, which contain as the kernel products of the Bessel and modified Bessel functions. Mapping properties and invertibility in Lebesgue spaces are studied for these operators. Relationships with the Kontorovich–Lebedev and Fourier cosine transforms are established. Inversion theorems are proved. As an application, a solution of the initial value problem for the fourth order partial differential equation, involving the Laplacian is presented.
Disclosure statement
No potential conflict of interest was reported by the author.
Funding
The work was partially supported by CMUP [UID/MAT/00144/2013], which is funded by FCT (Portugal) with national (MEC) and European structural funds through the programs FEDER, under the partnership agreement PT2020.