# zbMATH — the first resource for mathematics

Results on Colombeau product of distributions. (English) Zbl 0937.46030
Let $$x_+ = \max (x,0)$$, $$x_- = (-x)_+$$. The Colombeau products of the distributions $$x^a_+,x^b_-$$ and $$\delta ^{(p)}$$ are determined in the paper. More exactly, the following formulas are proved: $$x^p_+ \cdot \delta ^{(p)}=(-1)^p p!\delta /2$$, $$x^p_- \cdot \delta ^{(p)} = p!\delta /2$$, $$x^p\delta ^{(p)} = (-1)^p p!\delta$$ for any $$p\in \mathbb N_0$$, $$x^a_+ \cdot x^b_- = \Gamma (a+1)\Gamma (b+1)\delta /2$$, if $$-a, - b \notin \mathbb N$$, $$a+b+1=0$$. The same formulas hold if the regularized model product of distributions is considered. The quoted formulas are known with a more special product. The results are generalized for distributions in $$\mathbb R^m$$.

##### MSC:
 46F10 Operations with distributions and generalized functions
Full Text: