content_image/298930.jpg content_image/298925.jpg content_image/298926.jpg content_image/298927.jpg
(3.2) and (3.3), we have the following kinetic equation 

<img src='content_image/298930.jpg'>

By the setting of Problem 1, using equalities (3.1), (3.4) and the fact that a$_{jk}$ ( x ) is zero outside of D, we conclude that the function u ( x, ξ ) is known for ( x, ξ ) ∈ ∂D × R n $_{0}$. Then it is easy to see that the uniqueness of the solution of Problem 1 follows from the uniqueness of the solution of the following problem: 

Problem 2 Determine a matrix-valued function ( a$_{jk}$ ), (2 ≤ j, k ≤ n ) from equation (3.5) provided that u ( x, ξ ) is known for ( x, ξ ) ∈ ∂D × R n $_{0}$. 

In order to prove the uniqueness for Problem 2, it is sufficient to assume 

<img src='content_image/298925.jpg'>

## 4. APPLICATION OF THE FOURIER TRANSFORM TO PROBLEM 2 

In this section, we present three lemmata which describe some important prop- erties of the function u ( x, ξ ) and its Fourier transform. The proofs are given in Appendix. The Fourier transform F ( I ) of a function I ( x, ξ ) ∈ L$_{1}$ ( R 1 ξ ) with re- spect to the variable ξ 1 is defined by 

where η is the dual variable of ξ $^{1}$. Henceforth we set 

<img src='content_image/298926.jpg'>

<img src='content_image/298927.jpg'>

