Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

Online
ISSN
1435-5337
See all formats and pricing
More options …
Volume 28, Issue 2

Issues

Sampling and interpolation on some nilpotent Lie groups

Vignon Oussa
Published Online: 2014-09-09 | DOI: https://doi.org/10.1515/forum-2014-0035

Abstract

Let N be a non-commutative, simply connected, connected, two-step nilpotent Lie group with Lie algebra 𝔫 such that 𝔫=𝔞𝔟𝔷, [𝔞,𝔟]𝔷, the algebras 𝔞,𝔟,𝔷 are abelian, 𝔞=- span {X1,X2,...,Xd}, and 𝔟=- span {Y1,Y2,...,Yd}. Also, we assume that det[[Xi,Yj]]1i,jd is a non-vanishing homogeneous polynomial in the unknowns Z1,...,Zn-2d where {Z1,...,Zn-2d} is a basis for the center of the Lie algebra. Using well-known facts from time-frequency analysis, we provide some precise sufficient conditions for the existence of sampling spaces with the interpolation property, with respect to some discrete subset of N. The result obtained in this work can be seen as a direct application of time-frequency analysis to the theory of nilpotent Lie groups. Several explicit examples are computed. This work is a generalization of recent results obtained for the Heisenberg group by Currey and Mayeli in [Rocky Mountain J. Math. 42 (2012), no. 4, 1135–1151].

Keywords: Sampling; interpolation; nilpotent Lie groups; representations

MSC: 22E25; 22E27

About the article

Received: 2014-02-23

Revised: 2014-07-07

Published Online: 2014-09-09

Published in Print: 2016-03-01


Citation Information: Forum Mathematicum, Volume 28, Issue 2, Pages 255–273, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2014-0035.

Export Citation

© 2016 by De Gruyter.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Didier Arnal, Bradley Currey, and Béchir Dali
Journal of Fourier Analysis and Applications, 2019
[2]
Vignon Oussa
Journal of Functional Analysis, 2017

Comments (0)

Please log in or register to comment.
Log in