Using coherent states of the Weyl-Heisenberg algebra hN , extended Voros products and Moyal brakets are derived. The covariance of Voros product under canonical transformations is discussed. Star product related to BarutGirardello coherent states of the Lie algebra su(1, 1) is also considered. The star eigenvalue problem of singular harmonic osillator is investigated.

An algebraic treatment of shape-invariant potentials is discussed. By introducing an operator which reparametrizes wave functions, the shape-invariance condition can be related to a generalized Heisenberg-Weyl algebra. It is shown that this makes it possible to define a coherent state associated with the shape-invariant potentials.

We introduce the notion of square integrable group representation modulo a relatively central subgroup and, establishing a link with square integrable projective representations, we prove a generalization of a classical theorem of Duflo and Moore. As an example, we apply the results obtained to the Weyl-Heisenberg group.

We investigate a class of algebras that provides multiparameter versions of both quantum symplectic space and quantum Euclidean 2n-space. These algebras encompass the graded quantized Weyl algebras, the quantized Heisenberg space, and a class of algebras introduced by Oh. We describe the structure of the prime and primitive ideals of these algebras. Other structural results include normal separ...

The aim of this article is to construct à la Perelomov and à la Barut–Girardello coherent states for a polynomial Weyl-Heisenberg algebra. This generalized Weyl-Heisenberg algebra, noted A{κ}, depends on r real parameters and is an extension of the Aκ one-parameter algebra (Daoud M and Kibler M R 2010 J. Phys. A: Math. Theor. 43 115303) which covers the cases of the su(1, 1) algebra (for κ > 0)...

Deep convolutional neural networks (CNNs) used in practice employ potentially hundreds of layers and 10,000s of nodes. Such network sizes entail significant computational complexity due to the large number of convolutions that need to be carried out; in addition, a large number of parameters needs to be learned and stored. Very deep and wide CNNs may therefore not be well suited to applications...

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...

This paper is concerned with generalizations and specific applications of the coorbit space theory based on group representations modulo quotients that has been developed quite recently. We show that the general theory applied to the affine Weyl–Heisenberg group gives rise to families of smoothness spaces that can be identified with α-modulation spaces.

We discuss stable, overcomplete, non-orthogonal phase-space expansions with respect to generalized coherent states. The key concepts are Weyl-Heisenberg frames and quantitative measures of phase-space localization. On an abstract level, we introduce and investigate the localization of general frames.

We prove Hausdorff-Young inequality for the Fourier transform connected with Riemann-Liouville operator. We use this inequality to establish the uncertainty principle in terms of entropy. Next, we show that we can derive the Heisenberg-Pauli-Weyl inequality for the precedent Fourier transform.