On the Duality of Regular and Local Functions
نویسنده
چکیده
In this paper, we relate Poisson’s summation formula to Heisenberg’s uncertainty 1 principle. They both express Fourier dualities within the space of tempered distributions and 2 these dualities are furthermore the inverses of one another. While Poisson’s summation 3 formula expresses a duality between discretization and periodization, Heisenberg’s 4 uncertainty principle expresses a duality between regularization and localization. We define 5 regularization and localization on generalized functions and show that the Fourier transform 6 of regular functions are local functions and, vice versa, the Fourier transform of local 7 functions are regular functions. 8 9
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