Index transforms with the square of Bessel functions

2015/09/29 by Yakubovich, Semyon
#33C10 #44A05 #44A15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1509.08723

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.

Related

• New index transforms with the product of Bessel functions
• New index transforms of the Lebedev- Skalskaya type
• Lebedev's type index transforms with the modified Bessel functions
• Index transforms with Weber type kernels
• Discrete index transformations with squares of Bessel functions