  The quantum Euclidean space R_{q}^{N} is a kind of noncommutative space which
is obtained from ordinary Euclidean space R^{N} by deformation with parameter
q. When N is odd, the structure of this space is similar to R_{q}^{3}.
Motivated by realization of R_{q}^{3} by differential operators in R^{3}, we
give such realization for R_{q}^{5} and R_{q}^{7} cases and generalize our
results to R_{q}^{N} (N odd) in this paper, that is, we show that the algebra
of R_{q}^{N} can be realized by differential operators acting on C^{infinite}
functions on undeformed space R^{N}.
