(3.2) and (3.3), we have the following kinetic equation 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 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 u ( x, ξ ) = 0, ( x, ξ ) ∈ ∂D × R n $_{0}$. (3.6) F { I ( x, ξ ) } = ̂ I ( $_{x, η, ξ}$′ ) := ∫ ∞ −∞ I ( x, ξ 1 $_{, ξ}$′ ) e − √ − 1 ξ $^{$^{1}$η}$dξ $^{1}$, ∂$_{x}$ s = ∂ ∂x$_{s}$ , ∂$_{η}$ = ∂ ∂η , ∂$_{ξ}$ j = ∂ ∂ξ j , ∂ β ξ = ∂ β$_{1}$ ξ 1 · · · ∂ β$_{n}$ ξ n , | β | = β$_{1}$ + ... + β$_{n}$, ∂ β ′ ξ ′ = ∂ β$_{2}$ ξ 2 · · · ∂ β$_{n}$ ξ n , ∣ $_{β}$′ ∣ = β$_{2}$ + ... + β$_{n}$. 5 4. APPLICATION OF THE FOURIER TRANSFORM TO PROBLEM 2 n ∑ j =1 ξ j ∂u ∂x j − n ∑ j,k,s =1 Γ s $_{jk}$( x ) ξ $^{k}$ξj ∂u ∂ξ s = n ∑ j,k =2 a$_{jk}$ ( x ) ξ $^{k}$ξ$^{j}$. (3.5)