caa a22 4500 469065249 CHVBK 20180323132906.0 cr unu---uuuuu 170328e19920601xx s 000 0 eng 10.1007/BF02723177 doi (NATIONALLICENCE)springer-10.1007/BF02723177 A discretization of the continuous fourier transform [Elektronische Daten] [R. Campos, L. Juárez] Summary: A finite representation of the continuous Fourier transform is obtained in a linear space of dimensionN for the Hermite functions by using some properties of the Hermite polynomialsH N (x) and its zeros. TheN-dimensional vectors representing a Hermite function and its Fourier-trnasformed function converge to their exact continuous values whenN→∞. The genericN×N matrix representing the kernel of the continuous transform exp [−ipx], preserves the conspicuous properties of this function, and their entries approach the values that this kernel takes atp=x j andx=x k , wherex j andx k are two zeros ofH N (x) whenN→∞. These properties lead to propose this kind of matrices as finite representations of the kernel of the continuous Fourier transform for functions other than the Hermite ones, yielding certain quadrature formula for this transform. Some numerical examples of this application are shown and they are compared with those obtained through standard procedures. Società Italiana di Fisica, 1992 02.60 nationallicence Numerical approximation and analysis nationallicence 02.30.Gp nationallicence Special functions nationallicence 03.65 nationallicence Quantum theory nationallicence quantum mechanics nationallicence Campos R. Escuela de Física y Matemáticas, Universidad Michoacana, 58060, Morelia, Michoacán, México aut Juárez L. Escuela de Física y Matemáticas, Universidad Michoacana, 58060, Morelia, Michoacán, México aut Il Nuovo Cimento B (1971-1996) Società Italiana di Fisica 107/6(1992-06-01), 703-711 107:6<703 1992 107 40764 https://doi.org/10.1007/BF02723177 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02723177 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Campos R. Escuela de Física y Matemáticas, Universidad Michoacana, 58060, Morelia, Michoacán, México aut NATIONALLICENCE 700 1- Juárez L. Escuela de Física y Matemáticas, Universidad Michoacana, 58060, Morelia, Michoacán, México aut NATIONALLICENCE 773 0- Il Nuovo Cimento B (1971-1996) Società Italiana di Fisica 107/6(1992-06-01), 703-711 107:6<703 1992 107 40764 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer