Some distributional products with relativistic invariance.
Using a description of the topology of the spaces ( open convex subset of ) via the Fourier transform, namely their analytically uniform structures, we arrive at a formula describing the convex hull of the singular support of a distribution , . We give applications to a class of distributions satisfyingfor all .
Let and be distributions in and let be an infinitely differentiable function with , (or ). It is proved that if the neutrix product exists and equals , then the neutrix product exists and equals .
We introduce certain spaces of sequences which can be used to characterize spaces of functions of exponential type. We present a generalized version of the sampling theorem and a "nonorthogonal wavelet decomposition" for the elements of these spaces of sequences. In particular, we obtain a discrete version of the so-called φ-transform studied in [6] [8]. We also show how these new spaces and the corresponding decompositions can be used to study multiplier operators on Besov spaces.