2024-08-15T14:41:06Zhttps://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/335692021-06-24T07:21:35Zcom_10324_22154com_10324_954com_10324_894col_10324_22155
Celeghini, Enrico
Gadella Urquiza, Manuel
Olmo Martínez, Mariano Antonio del
2018
Producción Científica
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.
application/pdf
http://uvadoc.uva.es/handle/10324/33569
eng
MDPI
Hermite Functions, Lie Groups and Fourier Analysis
info:eu-repo/semantics/article
TEXT
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