Two-dimensional dirac delta reconsidered
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Distribution theory continues to be of significant importance in many branches of applied mathematics and especially within the research activities of theoretical and applied physicists. It is the belief of the author that the Dirac delta functional offers enormous impact in fostering advances within distribution theory together with its applications. Whenever one requires an example of a singular, ultra or new generalized function, a version of the Dirac delta satisfies that need. In this paper we have collected several very recent and important results for the Dirac delta and formulated them within a two-dimensional domain. We then go on and graph a three-dimensional version of the result implementing the software, Pro-Matlab. Within many branches of signal analysis the geometrical aspects of a particular mathematical concept are of paramount importance to the user. For example, when one implements a transform as a filter, the geometrical considerations give strong evidence of the utility of the filter for the particular application. We have also included a preliminary beginning for considering wavelet transforms applied to distributions.
Key wordsrapid-descent test functions tempered distributions Fourier-transforms convolutions Stieltjes transforms Hankel transforms wavelet transforms
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