@Article{JPDE-7-183,
author = {Jiang Yaping},
title = {The Fourier Transform and Its Weyl Symbol on Two-step Nilpotent Lie Groups},
journal = {Journal of Partial Differential Equations},
year = {1994},
volume = {7},
number = {2},
pages = {183--192},
abstract = { In this paper, we give all equivalence classes of irreducible unitary representations for the group H_n &#8855 R^m thereby formulate the Fourier transform on H_n &#8855 R^m (n &#8805 0, m &#8805 0}, which naturally unifies the Fourier transform between the Euclidean group and the Heisenberg group, more generally, between Abelian groups and two-step nilpotent Lie groups. Moreover, by the Plancberel formula for H_n &#8855 R^m we produce the Weyl symbol association with functions of the harmonic oscillator so that to derive the heat kernel on H_n &#8855 R^m.},
issn = {2079-732X},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jpde/5681.html}
}