Related papers: Sampling in unitary invariant subspaces associated…
We generalize the Cauchy-Davenport theorem to locally compact groups.
In this paper the inverse of the quaternionic Fourier transform on locally compact abelian groups is verified.
In this paper we use the $Z-$decomposition as a tool to find locally symmetric left invariant Riemannian metrics on some Lie groups. For this purpose, we need to compute the spectrum of the curvature operator. Since the study of this…
This paper is devoted to the study of geometry properties of wavelet and Riesz wavelet sets on locally compact abelian groups. The catalyst for our research is a result by Wang ([32], Theorem 1.1) in the Euclidean wavelet theory. Here, we…
The bracket map was originally considered for locally compact abelian groups. In this work we extend the study of bracket maps to the noncommutative setting, providing characterizations of bases and frames for cyclic subspaces of the…
This thesis is devoted to the study of the interactions existing between the algebraic structure of locally compact groups and the properties of their continuous unitary representations, with a special emphasis on the Type I groups. On the…
Equivariant T-duality triples of locally compact abelian groups are considered. The motivating example dealing with the group $\R^n$ containing a lattice $\Z^n$ comes with an isomorphism in twisted equivariant K-theory.
Sampling theory concerns the problem of reconstruction of functions from the knowledge of their values at some discrete set of points. In this paper we derive an orthogonal sampling theory and associated Lagrange interpolation formulae from…
This thesis is devoted to algorithmic aspects of the implementation of Cartan's moving frame method to the problem of the equivalence of submanifolds under a Lie group action. We adopt a general definition of a moving frame as an…
Assume that samples of a filtered version of a function in a shift-invariant space are avalaible. This work deals with the existence of a sampling formula involving these samples and having reconstruction functions with compact support.…
In this paper we consider some Lie groups in complexified Clifford algebras. Using relations between operations of conjugation in Clifford algebras and matrix operations we prove isomorphisms between these groups and classical matrix groups…
In this paper, we define locally convex vector spaces of weighted vector fields and use them as model spaces for Lie groups of weighted diffeomorphisms on Riemannian manifolds. We prove an easy condition on the weights that ensures that…
For a closed locally symmetric space M=\Gamma\G/K and a representation of G we consider the push-forward of the fundamental class in the homology of the linear group and a related invariant in algebraic K-theory. We discuss the…
The control of bilinear systems has attracted considerable attention in the field of systems and control for decades, owing to their prevalence in diverse applications across science and engineering disciplines. Although much work has been…
We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…
Given a monoidal probabilistic theory -- a symmetric monoidal category $\mathcal{C}$ of systems and processes, together with a functor $\mathbf{V}$ assigning concrete probabilistic models to objects of $\mathcal{C}$ -- we construct a…
Our paper begins with a revision of spectral theory for commutative Banach algebras, which enables us to prove the $L^p_{\omega}-$conjecture for locally compact abelian groups. We follow an alternative approach to the one known in the…
We compute the invariant subspace of the rational group ring of a surface, truncated by powers of the augmentation ideal, under the action of the mapping class group. The surface is compact, oriented with one boundary component. This…
A remarkable number of different numerical algorithms can be understood and analyzed using the concepts of symmetric spaces and Lie triple systems, which are well known in differential geometry from the study of spaces of constant curvature…
We present sampling theorems for reproducing kernel Banach spaces on Lie groups. Recent approaches to this problem rely on integrability of the kernel and its local oscillations. In this paper we replace the integrability conditions by…