Abstract
In the present paper, we study an equation of the form \(\int_{0}^{r}T^\alpha_yf(x)x^{2\alpha+1}\,dx=0, \qquad |y|< R-r, \quad 0<r<R,\) where \(\alpha>-1/2\) , \(T^\alpha_y\) is the generalized Bessel translation operator, and \(f\) is an even function locally integrable with respect to the measure \(|x|^{2\alpha+1}\,dx\) on the interval \((-R,R)\) . A description of the solutions of this equation in the form of series in special functions is obtained. Based on this result, we completely study the existence of a nonzero solution of a system of two such equations.
