On the General Solution of the Ultrahyperbolic Bessel Operator

摘要

We study the general solution of equation □B,cku(x)=f(x), where □B,ck is the ultrahyperbolic Bessel operator iterated k-times and is defined by □B,ck=[(1/c2)(Bx1+Bx2+⋯+Bxp)−(Bxp+1+⋯+Bxp+q)],  p+q=n, n is the dimension of ℝn+={x:x=(x1,x2,…,xn),  x1>0,…,xn>0}, Bxi=∂2/∂xi2+(2vi/xi)(∂/∂xi), 2vi=2βi+1, βi>−1/2, xi>0 (i=1,2,…,n), f(x) is a given generalized function, u(x) is an unknown generalized function, k is a nonnegative integer, c is a positive constant, and x∈Rn+.