On the General Solution of the Ultrahyperbolic Bessel Operator
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=2β...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2011-01-01
|
| Series: | Mathematical Problems in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2011/579645 |
| Summary: | 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+. |
|---|---|
| ISSN: | 1024-123X 1563-5147 |