Convolution of Ultradistributions and Field Theory
C.G.Bollini, T.Escobar, M.C.Rocca
TL;DR
This paper introduces a comprehensive definition of convolution for Tempered Ultradistributions, extending existing concepts and providing examples and applications in field theory.
Contribution
It generalizes the convolution of ultradistributions, linking it to Fourier transforms and demonstrating its use in field theory contexts.
Findings
Defined convolution for arbitrary Tempered Ultradistributions.
Connected ultradistribution convolution with Fourier transform products.
Reproduced known results in ultradistribution convolution and singular products.
Abstract
In this work, a general definition of Convolution between two arbitrary Tempered Ultradistributions is given. When one of the Tempered Ultradistributions is rapidly decreasing this definition coincides with the definition of J. Sebastiao e Silva. The product of two arbitrary distributions of exponential type is defined via the Convolution of its corresponding Fourier Transforms. Several examples of Convolution of two Tempered Ultradistributions and singular products are given. In particular, we reproduce the results obtained by A. Gonzales Dominguez and A. Bredimas.
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Taxonomy
TopicsMatrix Theory and Algorithms · Algebraic and Geometric Analysis · Mathematical and Theoretical Analysis