q-deformed Fourier Theory
Abstract
We solve the problem of Fourier transformation for the one-dimensional -deformed Heisenberg algebra. Starting from a matrix representation of this algebra we observe that momentum and position are unbounded operators in the Hilbert space. Therefore, in order to diagonalise the position operator in a momentum eigenbasis we have to study self-adjoint extensions of these operators. It turns out that there exist a whole family of such extensions for the position operator. This leads, correspondingly, to a one-parametric family of Fourier transformations. These transformations, which are related to continued fractions, are constructed in terms of -deformed trigonometric functions. The entire family of the Fourier transformations turns out to be characterised by an elliptic function.
Keywords
Cite
@article{arxiv.hep-th/9406168,
title = {q-deformed Fourier Theory},
author = {J. Schwenk},
journal= {arXiv preprint arXiv:hep-th/9406168},
year = {2008}
}
Comments
19, MPI-PhT/94-36 (14.July 1994)