On the General Solution of the Ultrahyperbolic Bessel Operator

摘要

We study the general solution of equation □~k_(B,c)= f(x), where □~k_(B,c) is the ultrahyperbolic Bessel operator iterated k-times and is defined by □~k_(B,c)= [(1/c~2)(B_(x1) + B_(x2) +…+B_(x1)-(B_(xp+1)+…+ B_(xp+q)]~k, p + q = n, n is the dimension of R~+_n = {x : x = (x1,x2,…,xn), x >0,…,x_n > 0},B_(xi) = ∂~2/∂x~2_I+(2v_I/x_I)(∂/∂x_I),2vi = 2β_I + 1,β_I, > -1/2, x_I >0(I = 1,2,…,n), f(x) is a given generalized function, u(x) is an unknown generalized function, A: is a nonnegative integer, c is a positive constant, and x∈R~+_n.