Corpus ID: 119140363

Uniqueness of the group Fourier transform on certain nilpotent Lie groups

  title={Uniqueness of the group Fourier transform on certain nilpotent Lie groups},
  author={Arup Kr. Chattopadhyay and Deb Kumar Giri and R. K. Srivastava},
  journal={arXiv: Functional Analysis},
In this article, we prove that if the group Fourier transform of certain integrable functions on the Heisenberg motion group (or step two nilpotent Lie groups) is of finite rank, then the function is identically zero. These results can be thought as an analogue to the Benedicks theorem that dealt with the uniqueness of the Fourier transform of integrable functions on the Euclidean spaces. 
1 Citations
Heisenberg uniqueness pairs for the Fourier transform on the Heisenberg group
In this article, we prove that (unit sphere, non-harmonic cone) is a Heisenberg uniqueness pair for the symplectic Fourier transform on $\mathbb C^n.$ We derive that spheres as well as non-harmonicExpand


Classical analysis and nilpotent Lie groups
Classical Fourier analysis has an exact counterpart in group theory and in some areas of geometry. Here I’ll describe how this goes for nilpotent Lie groups and for a class of Riemannian manifoldsExpand
Fundamental solutions for a class of hypoelliptic PDE
We introduce a class of nilpotent Lie groups which arise naturally from the notion of composition of quadratic forms, and show that their standard sublaplacians admit fundamental solutions analogousExpand
On theorems of Beurling and Hardy for certain step two nilpotent groups
In this paper we prove Hardy's theorem and a version of Cowling–Price theorem for all step two nilpotent Lie groups using Beurling's theorem on Euclidean space. Also a version of Beurling's theoremExpand
Representations of nilpotent Lie groups and their applications
Preface 1. Elementary theory of nilpotent Lie groups and Lie algebras 2. Kirillov theory 3. Parametrization of coadjoint orbits 4. Plancherel formula and related topics 5. Discrete cocompactExpand
Singular spherical maximal operators on a class of two step nilpotent lie groups
LetHn≅ℝ2n⋉ℝ be the Heisenberg group and letμt be the normalized surface measure for the sphere of radiust in ℝ2n. Consider the maximal function defined byM f=supt>0|f*μt|. We prove forn≥2 thatMExpand
CONTENTSIntroduction § 1. Induced representations § 2. Representations of Lie algebras and infinitesimal group rings § 3. A special nilpotent group N § 4. Nilpotent Lie groups with one-dimensionalExpand
Beurling's theorem for nilpotent Lie groups
In this paper, we prove an analogue of Beurling’s theorem for an arbitrary simply connected nilpotent Lie group extending then earlier cases .
Benedicks’ theorem for the Heisenberg group
If $f$ is a compactly supported function on the Heisenberg group and the group Fourier transform $\hat{f}(\lambda)$ is a finite rank operator for all $\lambda$ then $f$ is the zero function.
Functions and their Fourier transforms with supports of finite measure for certain locally compact groups
Abstract It is well known that if the supports of a function f ϵ L1(Rd) and its Fourier transform \ tf are contained in bounded rectangles, then f = 0 almost everywhere. In 1974 Benedicks relaxed theExpand
Bounded K-spherical functions on Heisenberg groups
Abstract Let Hn be the (2n + 1)-dimensional Heisenberg group, and let K be a compact subgroup of Aut(Hn), the group of automorphisms of Hn. The pair (K, Hn) is called a Gelfand pair if LK1(Hn), theExpand