On the non-commutative neutrix product involving slowly varying functions.
The non-commutative neutrix product of the distributions and is proved to exist for and is evaluated for . The existence of the non-commutative neutrix product of the distributions and is then deduced for and evaluated for .
Let denote the non-quasianalytic class of Beurling type on an open set Ω in . For the surjectivity of the convolution operator is characterized by various conditions, e.g. in terms of a convexity property of the pair and the existence of a fundamental solution for μ or equivalently by a slowly decreasing condition for the Fourier-Laplace transform of μ. Similar conditions characterize the surjectivity of a convolution operator between ultradistributions of Roumieu type whenever . These...
We give sufficient conditions for the support of the Fourier transform of a certain class of weighted integrable distributions to lie in the region and .