Решение многомерного интегрального уравнения типа Абеля с функцией Бесселя–Клиффорда в ядре по пирамидальной области

Abstract

Целью работы является решение в замкнутой форме многомерного интегрального уравнения со специальной функцией в ядре. = The interest in such equations is caused by their applications to the problems on the reflection of waves on a rectilinear boundary and on a supersonic flow around spatial corners. Ya. Tamarkin obtained a well-known classical result on the solvability of the Abel integral equation in the space L a b 1 ,  of integrable functions on a finite interval [ , ] a b of the real line. By Tamarkin’s method the solution of the investigating equation in the closed form is established, and necessary and sufficient conditions for its solvability in the space of summable functions are given. The results generalize the well know findings for the multi-dimensional Abel type integral equation and the corresponding one-dimensional equations of the first kind.