Abstract
The singular ultrahyperbolic equation \((\Delta _{B_{\beta }})_y u=(\Delta _{B_{\gamma }})_x u\) is considered under the assumption that thefollowing Kipriyanov condition is satisfied: the fractional dimensions of all \(\Delta _{B_{\gamma }}\) -operators occurring in the equation are equal toone and the same positive number \(\sigma \) . Three typesof solutions of the radial Cauchy problem are studied, one of them is based on the \(\mathbb {T}\) -pseudotranslation operator, the generalized \(\mathbb {T}\) -translation, and S.A. Tersenov’s method fordetermining solutions of equations degenerating on the boundary. Poisson formulas for thesolution of the Cauchy problem for the Euler–Poisson–Darboux equation are given for variousparameter values in this equation.
