We introduce a systematic approach to the design, implementation and analysis of left-invariant evolution schemes acting on Gabor transform, primarily for applications in signal and image analysis. Within this approach we relate operators on signals to operators on Gabor transforms. In order to obtain a translation and modulation invariant operator on the space of signals, the corresponding ope...

We provide the explicit solutions of linear, left-invariant, diffusion equations and the corresponding resolvent equations on the 2D-Euclidean motion group SE(2) = R T. These parabolic equations are forward Kolmogorov equations for well-known stochastic processes for contour enhancement and contour completion. The solutions are given by group convolution with the corresponding Green’s functions...

We provide the explicit solutions of linear, left-invariant, diffusion equations and the corresponding resolvent equations on the 2D-Euclidean motion group SE(2) = R T. These parabolic equations are forward Kolmogorov equations for well-known stochastic processes for contour enhancement and contour completion. The solutions are given by group convolution with the corresponding Green’s functions...

We study the dynamics of magnetic flows on Heisenberg groups, investigating extent to which properties underlying Riemannian geometry are reflected in flow. Much analysis, including a calculation Mañé critical value, is carried out for $$(2n+1)$$ -dimensional groups endowed with any left invariant metric and exact, left-invariant field. In three-dimensional case, we obtain complete analysis lef...

In this paper, we study the set of homogeneous geodesics of a leftinvariant Finsler metric on Lie groups. We first give a simple criterion that characterizes geodesic vectors. As an application, we study some geometric properties of bi-invariant Finsler metrics on Lie groups. In particular a necessary and sufficient condition that left-invariant Randers metrics are of Berwald type is given. Fin...

In this paper, we describe a natural method to extend left invariant weights on C *-algebraic quantum groups. This method is then used to improve the invariance property of a left invariant weight. We also prove some kind of uniqueness result for left Haar weights on C *-algebraic quantum groups arising from algebraic ones.

This paper is devoted to the study of the Hamiltonian formulation of non-linear sigma models on supercoset targets. We calculate the Poisson brackets of left-invariant currents. Then we introduce the Hamiltonian of the system and determine the equations of motion for left-invariant currents. We also determine the charge corresponding to the invariance of the action under global left multiplicat...

A result from Gromov ensures the existence of a contact structure on any connected non-compact odd dimensional Lie group. But in general such structures are not invariant under left translations. The problem of finding which Lie groups admit a left invariant contact structure (contact Lie groups), is then still wide open. We perform a ‘contactization’ method to construct, in every odd dimension...

We consider the efficient quantization of a class of non bandlimited signals, namely the class of discrete time signals that can be recovered from their decimated version. By definition, these signals are cwersampled and it is reasonable to expect that we can reap the same benefits of well known efficient A/D conversion techniques. Indeed, by using appropriate multirate reconstruction schemes, ...

This paper develops an approach to the transient analysis of adaptive filters with data normalization. Among other results, the derivation characterizes the transient behavior of such filters in terms of a linear time-invariant state-space model. The stability of the model then translates into the mean-square stability of the adaptive filters. Likewise, the steady-state operation of the model p...