In this paper a strong form of the Stone-von Neumann property of the Heisenberg representation is stated and proved. Several results in harmonic analysis are obtained as a consequence.

We study the variety of actions of a fixed (Chevalley) group on arbitrary geodesic, Gromov hyperbolic spaces. In high rank we obtain a complete classification. In rank one, we obtain some partial results and give a conjectural picture.

In an earlier paper, we considered a phenomenological action with unconventional supersymmetry. Here we consider a microscopic statistical picture which leads to exactly the same form for the action that was postulated before. We find that standard physics can be regained at low energy for fermions and gauge bosons, but that there are testable extensions of standard physics for fermions at high...

The dynamics of quantum expectation values is considered in a geometric setting. First, expectation values of the canonical observables are shown to be equivariant momentum maps for the action of the Heisenberg group on quantum states. Then, the Hamiltonian structure of Ehrenfest's theorem is shown to be Lie-Poisson for a semidirect-product Lie group, named the Ehrenfest group. The underlying P...

As the heat kernel plays an important role in many problems in harmonic analysis, an explicit usable expression is very much desirable. An explicit expression for the heat kernel for the Heisenberg group Hn = C ×R was obtained by Hulanicki [9] and by Gaveau [7]. Gaveau [7] also obtained the heat kernel for free nilpotent Lie groups of step two. Cygan [4] obtained the heat kernel for all nilpote...

in this paper we proved that every g-riesz basis for hilbert space $h$ with respect to $k$ by adding a condition is a riesz basis for hilbert $b(k)$-module $b(h,k)$. this is an extension of [a. askarizadeh,m. a. dehghan, {em g-frames as special frames}, turk. j. math., 35, (2011) 1-11]. also, we derived similar results for g-orthonormal and orthogonal bases. some relationships between dual fram...

A prominent hypothesis of hemispheric specialization for human speech and music states that the left and right auditory cortices (ACs) are respectively specialized for precise calculation of two canonically-conjugate variables: time and frequency. This spectral-temporal asymmetry does not account for sex, brain-volume, or handedness, and is in opposition to closed-system hypotheses that restric...

Design of Weyl-Heisenberg sets of waveforms for robust orthogonal frequency division multiplexing (OFDM) has been the subject of a considerable volume of work. In this paper, a complete parameterization of orthogonal Weyl-Heisenberg sets and their corresponding biorthogonal sets is given. Several examples of Weyl-Heisenberg sets designed using this parameterization are presented, which in simul...

We prove a fundamental case of a conjecture of the first author which expresses the homology of the extension of the Heisenberg Lie algebra by C[t]/(t) in terms of the homology of the Heisenberg Lie algebra itself. More specifically, we show that both the 0 and k + 1 x-graded components of homology of this extension of the 3-dimensional Heisenberg Lie algebra have dimension 3 by constructing a ...

1. Fourier transform on Rn 1 2. Fourier analysis on the Heisenberg group 2 2.1. Representations of the Heisenberg group 2 2.2. Group Fourier transform 3 2.3. Convolution and twisted convolution 5 3. Hermite and Laguerre functions 6 3.1. Hermite polynomials 6 3.2. Laguerre polynomials 9 3.3. Special Hermite functions 9 4. Group Fourier transform of radial functions on the Heisenberg group 12 Ref...