Hermite functions and fourier series

18Citations
Citations of this article
12Readers
Mendeley users who have this article in their library.

Abstract

Using normalized Hermite functions, we construct bases in the space of square integrable functions on the unit circle (L2 (C)) and in l2 (Z), which are related to each other by means of the Fourier transform and the discrete Fourier transform. These relations are unitary. The construction of orthonormal bases requires the use of the Gramm–Schmidt method. On both spaces, we have provided ladder operators with the same properties as the ladder operators for the one-dimensional quantum oscillator. These operators are linear combinations of some multiplication-and differentiation-like operators that, when applied to periodic functions, preserve periodicity. Finally, we have constructed riggings for both L2 (C) and l2 (Z), so that all the mentioned operators are continuous.

Cite

CITATION STYLE

APA

Celeghini, E., Gadella, M., & Del Olmo, M. A. (2021). Hermite functions and fourier series. Symmetry, 13(5). https://doi.org/10.3390/sym13050853

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free