RT info:eu-repo/semantics/article
T1 Hermite Functions, Lie Groups and Fourier Analysis
A1 Celeghini, Enrico
A1 Gadella Urquiza, Manuel
A1 Olmo Martínez, Mariano Antonio del
K1 Análisis de Fourier
K1 Mecánica cuántica
K1 Fourier analysis
K1 Quantum mechanics
AB 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.
PB MDPI
YR 2018
FD 2018
LK http://uvadoc.uva.es/handle/10324/33569
UL http://uvadoc.uva.es/handle/10324/33569
LA eng
NO Entropy, 2018, 20 (11), 816;
NO Producción Científica
DS UVaDOC
RD 15-ago-2024