It is well known that (U(p,q),Hₙ) is a generalized Gelfand pair. Applying the associated spectral analysis, we prove a theorem of Wiener Tauberian type for the reduced Heisenberg group, which generalizes a known result for the case p = n, q = 0.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-2-1,
author = {Linda Saal},
title = {A Wiener type theorem for (U(p,q),Hn)},
journal = {Colloquium Mathematicae},
volume = {120},
year = {2010},
pages = {169-180},
zbl = {1193.43008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-2-1}
}
Linda Saal. A Wiener type theorem for (U(p,q),Hₙ). Colloquium Mathematicae, Tome 120 (2010) pp. 169-180. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-2-1/