We present a notion of frame multiresolution analysis on the Heisenberg group, abbreviated by FMRA, and study its properties. Using the irreducible representations of this group, we shall define a sinc-type function which is our starting point for obtaining the scaling function. Further, we shall give a concrete example of a wavelet FMRA on the Heisenberg group which is analogous to the Shannon...

We describe a family of quantum states the Schr\"odinger cat type as superpositions harmonic oscillator coherent with coefficients defined by quadratic Gauss sums. These emerge eigenfunctions lowering operators obtained after canonical transformations Heisenberg-Weyl algebra associated ordinary and fractional Fourier transformation. The first member this is given well known Yurke-Stoler state.

The innationary scenarios suggested by the duality properties of string cosmol-ogy in the Brans-Dicke (or String) frame are shown to correspond to accelerated contraction (deeation) when Weyl-transformed to the Einstein frame. We point out that the basic virtues of innation (solving the atness and horizon problems, amplifying vacuum uctuations) have physically equivalent counterparts in the de-...

In this paper, we study several weighted norm inequalities for the Opdam–Cherednik transform. We establish different versions of Heisenberg–Pauli–Weyl inequality particular, give an extension using weights with exponents and present a variation that incorporates [Formula: see text]-norms Also, prove version Hardy–Littlewood Finally, other variations such as Nash-type Clarkson-type

Classes of non-Hermitian operators that have only real eigenvalues are presented. Such operators appear in quantum mechanics and are expressed in terms of the generators of the Weyl-Heisenberg algebra. For each non-Hermitian operator A, a Hermitian involutive operator Ĵ such that A is Ĵ-Hermitian, that is, ĴA = AĴ , is found. Moreover, we construct a positive definite Hermitian Q such that A is...

New quantal states which interpolate between the coherent states of the Heisenberg-Weyl (W3) and SU(1,1) algebras are introduced. The interpolating states are obtained as the coherent states of a closed and symmetric algebra which interpolates between the W3 and SU(1,1) algebras. The overcompleteness of the interpolating coherent states is established. Differential operator representations in s...

Let H be the general, reduced Heisenberg group. Our main result establishes the inverse-closedness of a class of integral operators acting on Lp(H), given by the off-diagonal decay of the kernel. As a consequence of this result, we show that if α1I+Sf , where Sf is the operator given by convolution with f , f ∈ Lv(H), is invertible in B(Lp(H)), then (α1I + Sf )−1 = α2I + Sg, and g ∈ Lv(H). We p...

Abstract. A curvature-type tensor invariant called quaternionic contact (qc) conformal curvature is defined on a qc manifolds in terms of the curvature and torsion of the Biquard connection. The discovered tensor is similar to the Weyl conformal curvature in Riemannian geometry and to the Chern-Moser invariant in CR geometry. It is shown that a qc manifold is locally qc conformal to the standar...