The Hilbert Space Representations for SOq(3)-symmetric Quantum Mechanics

The SOq(N) - Symmetric Harmonic Oscillator on the Quantum Euclidean Space RN q and its Hilbert Space Structure” Int

Realization of the Three-dimensional Quantum Euclidean Space by Differential Operators

The three-dimensional quantum Euclidean space is an example of a non-commutative space that is obtained from Euclidean space by q-deformation. Simultaneously, angular momentum is deformed to soq(3), it acts on the q-Euclidean space that becomes a soq(3)-module algebra this way. In this paper it is shown, that this algebra can be realized by differential operators acting on C∞ functions on R. On...

Multiresolution wavelet analysis of integer scale Bessel functions

We identify multiresolution subspaces giving rise via Hankel transforms to Bessel functions. They emerge as orthogonal systems derived from geometric Hilbert-space considerations, the same way the wavelet functions from a multiresolution scaling wavelet construction arise from a scale of Hilbert spaces. We study the theory of representations of the C ∗-algebra Oν+1 arising from this multiresolu...

ar X iv : h ep - t h / 94 07 19 5 v 2 4 M ay 1 99 5 The Euclidean Hopf Algebra U q ( e N ) and its fundamental Hilbert space representations

We construct the Euclidean Hopf algebra Uq(e ) dual of Fun(Rq >⊳SOq−1(N)) by realizing it as a subalgebra of the differential algebra Diff(Rq ) on the quantum Euclidean space Rq ; in fact, we extend our previous realization [1] of Uq−1(so(N)) within Diff(R N q ) through the introduction of q-derivatives as generators of q-translations. The fundamental Hilbert space representations of Uq(e N ) t...

F eb 2 00 3 Representation of Semigroups in Rigged Hilbert Spaces : Subsemigroups of the Weyl - Heisenberg Group

This paper studies how differentiable representations of certain subsemigroups of the Weyl-Heisenberg group may be obtained in suitably constructed rigged Hilbert spaces. These semigroup representations are induced from a continuous unitary representation of the Weyl-Heisenberg group in a Hilbert space. Aspects of the rigged Hilbert space formulation of time asymmetric quantum mechanics are als...