On the Duality of Regular and Local Functions
AbstractIn this paper, we relate Poisson’s summation formula to Heisenberg’s uncertainty principle. They both express Fourier dualities within the space of tempered distributions and these dualities are also inverse of each other. While Poisson’s summation formula expresses a duality between discretization and periodization, Heisenberg’s uncertainty principle expresses a duality between regularization and localization. We define regularization and localization on generalized functions and show that the Fourier transform of regular functions are local functions and, vice versa, the Fourier transform of local functions are regular functions. View Full-Text
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Fischer, J.V. On the Duality of Regular and Local Functions. Mathematics 2017, 5, 41.
Fischer JV. On the Duality of Regular and Local Functions. Mathematics. 2017; 5(3):41.Chicago/Turabian Style
Fischer, Jens V. 2017. "On the Duality of Regular and Local Functions." Mathematics 5, no. 3: 41.
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