‎In this paper‎, ‎we study translation invariant surfaces in the‎ ‎3-dimensional Heisenberg group $rm Nil_3$‎. ‎In particular‎, ‎we‎ ‎completely classify translation invariant surfaces in $rm Nil_3$‎ ‎whose position vector $x$ satisfies the equation $Delta x = Ax$‎, ‎where $Delta$ is the Laplacian operator of the surface and $A$‎ ‎is a $3 times 3$-real matrix‎.

We present a comprehensive analysis of the convergence properties of the frame operators of Weyl-Heisenberg systems and shift-invariant systems, and relate these to the convergence of the Walnut representation. We give a deep analysis of necessary conditions and sufficient conditions for convergence of the frame operator. We show that symmetric, norm and unconditional convergence of the Walnut ...

We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenberg invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as well as in terms of lattice paths. We show that the Heisenberg invariant gives a...

Let H be a Heisenberg superalgebra. In this paper, the definition of biderivations and the properties of biderivations on Lie superalgebras are introduced. And some properties of biderivations on Heisenberg superalgebras are introduced by the definition of Heisenberg superalge-bras.

a generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by m. h. faroughi and r. ahmadi, is presented in this study. continuous resolution of the identity (cri) is introduced, a new family of cri is constructed, and a number of reconstruction formulas are obtained. also, new results are given on the duality of continuous fusion fram...

Definition. A Heisenberg group for a symplectic vector space (V, ω) is the Lie group with the underlying manifold V ×R and the multiplication (u, s)(v, t) = (u+ v, s+ t+ ω(u, v)/2) where u, v ∈ V and s, t ∈ R. The map t 7→ (0, t) is a Lie group homomorphism from R to the Heisenberg group. Its image coincides with the center of the Heisenberg group. The dimension of the Heisenberg group equals 2...

In this paper I shall present the construction of Weyl-Heisenberg superframes and density results related to the noncoherent case. A superframe is a collection of r-frames F = ff i ; i 2 Ig H1, : : : , F r = ff i ; i 2 Ig Hr all having the same countable index set I such that F = ff i f r i ; i 2 Ig is a frame for the Hilbert spaceH = H1 Hr. For the Weyl-Heisenberg superframes we set H1 = = Hr ...

The goal of the present paper is a short introduction to a general module frame theory in C*-algebras and Hilbert C*modules. The reported investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert bases, and of reconstruction of the frames by projections and other bounded module operators with suitable ranges. We...