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Convolution of n-Dimensional Tempered Ultradistributions and Field Theory

“…[3] for the one-dimensional case. For an immediate application of (4.1-4.3) we can evaluate the product of two arbitrary derivatives of a n-dimensional δ distribution.…”

Convolution of Lorentz Invariant Ultradistributions and Field Theory

“…In a earlier paper [3] we have shown the existence of the convolution of two one-dimensional tempered ultradistributions. In other paper ref.…”

“…[3] for the one-dimensional case. The Fourier antitransform of (6.11) defines the product of two distributions of exponential type.…”

Reflections on the q-Fourier transform and the q-Gaussian function

“…Here we will deal with complex q-exponentials, i.e., e q (ikx) for 1 ≤ q < 2 with k a real number (see ( [23]) space of tempered distributions is too restrictive. Instead, ultra-distributions satisfy that need [19], being continuous linear functionals defined on the space of entire functions rapidly decreasing on straight lines parallel to the real axis [19].…”

“…This situation was adequately remedied in [25], whose authors, by using tempered ultra-distributions [19,30], introduced a complex q-Fourier transform F (k, q) which exhibits nice properties and is one-to-one. In turn, this overcame a serious flaw of the original F q −definition, i.e., not being of the essential one-to-one nature [27].…”