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...

Investigating the favorable configurations for non-classical correlations preservation has remained a hotly debated topic last decade. In this regard, we present two-qubit Heisenberg spin chain system exposed to time-dependent external magnetic field. The impact of various crucial parameters, such as initial strength and angular frequency field along with state’s purity anisotropy spin-spin on ...

Affine control systems on the generalized Heisenberg Lie groups are studied. Controllability of this kind of class of systems on the generalized Heisenberg Lie group is established by relating to their associated bilinear part. AMS Subject Classification: 22E20

A characterization of the maximal abelian sub-algebras of matrix algebras that are normalized by the canonical representation of a finite Heisenberg group is given. Examples are constructed using a classification result for finite Heisenberg groups.

We investigate the relevance of admissibility criteria based on Plancherel measure for the characterization of tight Weyl-Heisenberg frames with integer oversampling. For this purpose we observe that functions giving rise to such Weyl-Heisenberg frames are admissible with regard to the action of a suitably defined type-I discrete group G. This allows to relate the construction of Weyl-Heisenber...

A discrete version of the Zak transform is defined and used to analyze discrete Weyl–Heisenberg frames, which are nonorthogonal systems in the space of square-summable sequences that, although not necessarily bases, provide representations of square-summable sequences as sums of the frame elements. While the general theory is essentially similar to the continuous case, major differences occur w...

in order to estimate the effects of the macrc~econornic indicators on the income distribution of iran, the time series data during the period of 1971-1991 were used. first the yammetric inequality indicators (the gini coefficients) were estimated for the years 1991-1972. the results show the lowest level of inequality in 1980 with g=0.42 and the highest level in 1982 with g=0.55. arzulysing the...