Timeline for Why is the Fourier transform so ubiquitous?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 15, 2020 at 20:20 | comment | added | Tom Copeland | Related: mathoverflow.net/questions/9834/… | |
| Feb 14, 2020 at 8:41 | comment | added | Tom Copeland | Central to the mystery of quantun mechanics is the interference of complex wave functions representing probability amplitudes. To speak in generalities of linear transformations, groups, and symmetries without accounting for interference effects is a sterile exercise w.r.t. characterizing QM and, more prosaically, coherent imaging systems. (When discussing conservation laws, invariants, and equivalencies, symmetries come to the forefront.) | |
| Feb 14, 2020 at 6:45 | comment | added | Tom Copeland | In Mathemagics, eqns. 51, 52, and 53 should have zero explicitly as the lower limits of integration of the integrals, identifying 51 as a Laplace convolution, 52 as a Laplace transform, and 53 as a Mellin transform evaluated at positive integers. | |
| Feb 14, 2020 at 6:05 | history | edited | Tom Copeland | CC BY-SA 4.0 |
Added ref
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| Feb 12, 2020 at 22:32 | comment | added | Tom Copeland | In addition to the Frenkel ref on the Langlands program in the linked MO-Q related to the Fourier-Mukai transform, there is the more recent paper "An analytic version of the Langlands correspondence for complex curves" by Etingof, Frenkel, and Kazhdan (arxiv.org/abs/1908.09677) eschewing sheaves for functions. | |
| Feb 11, 2020 at 23:58 | comment | added | Tom Copeland | A very important example of a Green/impulse response function is the sinc function, a central character in the Shannon sampling theorem and Cesaro summation of divergent series. | |
| Feb 11, 2020 at 23:53 | comment | added | Tom Copeland | Another variant is the Mellin transform which plays key roles in analytic number and interpolation theory and the realm of finite differences. | |
| Feb 11, 2020 at 23:36 | history | answered | Tom Copeland | CC BY-SA 4.0 |