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Title: Hermite Functions, Lie Groups and Fourier Analysis
Authors: Celeghini, Enrico
Gadella, Manuel
Olmo, Mariano A. del
Issue Date: 2018
Publisher: MDPI
Description: Producción Científica
Citation: Entropy, 2018, 20 (11), 816;
Abstract: 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.
Classification: Análisis de Fourier
Mecánica cuántica
Fourier analysis
Quantum mechanics
Peer Review: SI
Sponsor: Ministerio de Economía, Industria y Competitividad (Project MTM2014-57129-C2-1-P)
Junta de Castilla y León (programa de apoyo a proyectos de investigación - Ref. VA137G18)
Publisher Version:
Language: eng
Rights: info:eu-repo/semantics/openAccess
Appears in Collections:FM - Artículos de revista

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