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oai:uvadoc.uva.es:10324/335692025-03-26T19:10:17Zcom_10324_22154com_10324_954com_10324_894col_10324_22155

Celeghini, Enrico Gadella Urquiza, Manuel Olmo Martínez, Mariano Antonio del 2018-12-19T12:00:46Z 2018-12-19T12:00:46Z 2018 Entropy, 2018, 20 (11), 816; http://uvadoc.uva.es/handle/10324/33569 10.3390/e20110816 In this paper, we present recent results in harmonic analysis in the real line R and in the half-line R+ , which show a closed relation between Hermite and Laguerre functions, respectively, their symmetry groups and Fourier analysis. This can be done in terms of a unified framework based on the use of rigged Hilbert spaces. We find a relation between the universal enveloping algebra of the symmetry groups with the fractional Fourier transform. The results obtained are relevant in quantum mechanics as well as in signal processing as Fourier analysis has a close relation with signal filters. In addition, we introduce some new results concerning a discretized Fourier transform on the circle. We introduce new functions on the circle constructed with the use of Hermite functions with interesting properties under Fourier transformations. eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/4.0/ Attribution 4.0 International Hermite Functions, Lie Groups and Fourier Analysis info:eu-repo/semantics/article