Home Sinc-type functions on a class of nilpotent Lie groups
Article
Licensed
Unlicensed Requires Authentication

Sinc-type functions on a class of nilpotent Lie groups

  • Vignon Oussa EMAIL logo
Published/Copyright: January 14, 2014
Become an author with De Gruyter Brill
Author Information Explore this Subject
Advances in Pure and Applied Mathematics
From the journal Advances in Pure and Applied Mathematics Volume 5 Issue 1

Abstract.

Let N be a simply connected, connected nilpotent Lie group with the following assumptions. Its Lie algebra 𝔫 is an n-dimensional vector space over the reals. Moreover, 𝔫=π”·βŠ•π”ŸβŠ•π”ž, 𝔷 is the center of 𝔫, 𝔷=ℝZn-2dβŠ•β„Zn-2d-1βŠ•β‹―βŠ•β„Z1, π”Ÿ=ℝYdβŠ•β„Yd-1βŠ•β‹―βŠ•β„Y1, π”ž=ℝXdβŠ•β„Xd-1βŠ•β‹―βŠ•β„X1. Next, assume π”·βŠ•π”Ÿ is a maximal commutative ideal of 𝔫, [π”ž,π”Ÿ]βŠ†π”·, and det ([Xi,Yj])1≀i,j≀d is a non-trivial homogeneous polynomial defined over the ideal [𝔫,𝔫]βŠ†π”·. We do not assume that [π”ž,π”ž] is generally trivial. We obtain some precise description of band-limited spaces which are sampling subspaces of L2(N) with respect to some discrete set Ξ“. The set Ξ“ is explicitly constructed by fixing a strong Malcev basis for 𝔫. We provide sufficient conditions for which a function f is determined from its sampled values on (f(Ξ³))Ξ³βˆˆΞ“. We also provide an explicit formula for the corresponding sinc-type functions. Several examples are also computed in the paper.

Keywords: Sampling; interpolation; nilpotent Lie groups; representations
MSC: 22E25; 22E27

Funding source: Czech Ministry of Education

Award Identifier / Grant number: ERC CZ LL1203

The author thanks the anonymous reviewer for a careful and thorough reading. His suggestions and corrections greatly improved the quality of the paper.

Received: 2013-08-19
Revised: 2013-12-20
Accepted: 2013-12-20
Published Online: 2014-01-14
Published in Print: 2014-03-01

Β© 2014 by Walter de Gruyter Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. A note on generalized absolute CesΓ ro summability
  3. Sinc-type functions on a class of nilpotent Lie groups
  4. Some new general integral inequalities for h-convex and h-concave functions
  5. The construction of periodic unfolding operators on some compact Riemannian manifolds
  6. Integration operators from the space of Cauchy integral transforms to the Dirichlet space
https://doi.org/10.1515/apam-2013-0028
Keywords for this article
Sampling; interpolation; nilpotent Lie groups; representations

Articles in the same Issue

  1. Frontmatter
  2. A note on generalized absolute CesΓ ro summability
  3. Sinc-type functions on a class of nilpotent Lie groups
  4. Some new general integral inequalities for h-convex and h-concave functions
  5. The construction of periodic unfolding operators on some compact Riemannian manifolds
  6. Integration operators from the space of Cauchy integral transforms to the Dirichlet space
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 17.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/apam-2013-0028/html
Scroll to top button