New index transforms with the product of Bessel functions

作者：Yakubovich S^*

来源：Integral Transforms and Special Functions, 2015, 26(12): 939-955.

DOI：10.1080/10652469.2015.1070150

• index transforms
• Bessel functions
• modified Bessel functions
• Kontorovich-Lebedev transform
• Fourier transform
• Mellin transform

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.

• 出版日期2015-12-2