Results on the commutative neutrix convolution product of distributions. (English) Zbl 0812.46028

Fisher, Brian; Özçaḡ, Emin

Arch. Math., Brno 29, No. 1-2, 105-117 (1993).

Summary: Let \(f\), \(g\) be distributions in \({\mathcal D}'\) and let \(f_ n(x)= f(x)\tau_ n(x)\), \(g_ n(x)= g(x)\tau_ n(x)\), where \(\tau_ n(x)\) is a certain function which converges to the identity function as \(n\) tends to infinity. Then the commutative neutrix convolution product \(f\boxed{*} g\) is defined as the neutrix limit of the sequence \(\{f_ n * g_ n\}\), provided the limit exists. The neutrix convolution product \(\ln x_ - \boxed{*} x^ r_ +\) is evaluated for \(r= 0,1,2,\dots\), from which other neutrix convolution products are deduced.

MSC:

46F10	Operations with distributions and generalized functions
44A35	Convolution as an integral transform

Keywords:

commutative neutrix convolution product