R $^{d}$; it is also possible to consider a nonparametric class for α with restricted support, ¯ W . Of course without any restrictions ¯ W = R $^{d}$. Recall the differ- entiation operator, ∂ $^{m}$, for m = ( m$_{1}$, ...m$_{d}$ ˙ ) and denote by supp ( β, ∂ ) the set ∪ ∞ Σ m i $_{=0}$supp ( ∂ $^{m}$β ); where supp ( ∂ $^{m}$β ) is an open set where a continuous derivative ∂ $^{m}$β exists. Any point where β is zero belongs to this set if some finite-order partial continuous derivative of β is not zero at that point (and in some open neighborhood); for β itself supp ( β ) ≡ supp ( β, 0) . Define the functions with any ˜ α such that α$_{1}$α$_{2}$ ∈ F t ( A ) . Consider the case when α, β and thus γ are continuous. For any point x$_{0}$ if β ( x$_{0}$ ) = 0 , there is a neighborhood N ( x$_{0}$ ) where β = 0 , and division by β is possible. If β ( x$_{0}$ ) has a zero, it could only be of finite order and in some neighborhood, N ( x$_{0}$ ) ∈ supp ( ∂ $^{m}$β ) a representation holds for some continuous function η in S $^{∗}$, such that η > c$_{η}$ > 0 on supp ( η ) . Then η − $^{1}$γ in N ( x$_{0}$ ) is a non-zero continuous function; division of such a function by Π d i $_{=1}$( x$_{i}$ − x$_{0}$$_{i}$ ) m i in S ∗ is defined (Schwartz, 1967, pp. 125-126), thus division by β is defined in this neighborhood N ( x$_{0}$ ). For the β = η ( x )Π d i =1 ( x$_{i}$ − x$_{0}$$_{i}$ ) m i (7) α$_{1}$ = β − $^{1}$γI ( supp ( β, ∂ )) ; α$_{2}$ ( x ) =     1 for x ∈ supp ( β, ∂ ); ˜ α for x ∈ ¯ W \ ( supp ( β, ∂ )) (6) 39