The Grushin plane is a right quotient of the Heisenberg group. Heisenberg geodesics’ projections are solutions of an isoperimetric problem in the Grushin plane.

we derive whole series of new integral inequalities of the hardy-type, with non-conjugate exponents. first, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. general results are then applied to special hardy-type kernel and power weights. also, some estimates of weight functions and constant factors are obtained. ...

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 violations of Lorentz invariance, both for fermions...

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...

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...

Bell non-locality represents the ultimate consequence of quantum entanglement, fundamentally undermining classical tenet that spatially-separated degrees freedom possess objective attributes independently act their measurement. Despite its importance, probing in many-body systems is considered to be a formidable challenge, with computational cost scaling exponentially system size. Here we propo...

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...