Related papers: Harmonic Synthesis on Group Extensions

We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable…

In this paper we discuss large cardinals and compactness theorems in abelian group theory. More specifically, we generalize two classical compactness results for free abelian groups to the broader context of direct sums of cyclic groups.

The additivity with respect to exact sequences is notoriously a fundamental property of the algebraic entropy of group endomorphisms. It was proved for abelian groups by deeply exploiting their structure. On the other hand, a solvable…

Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…

Using techniques from TRO equivalence of masa bimodules we prove various transference results: We show that when $\alpha$ is a group homomorphism which pushes forward the Haar measure of $G$ to a measure absolutely continuous with respect…

This article continues a prior investigation of the authors with the goal of extending characterization results of convolutional tight frames from the context of cyclic groups to general finite abelian groups. The collections studied are…

The distributed synthesis problem is about constructing cor- rect distributed systems, i.e., systems that satisfy a given specification. We consider a slightly more general problem of distributed control, where the goal is to restrict the…

We revisit general arguments for the absence of exact continuous global symmetries in string compactifications and extend them to D-brane models. We elucidate the various ways approximate continuous global symmetries arise in the…

Chords in musical harmony can be viewed as objects having shapes (major/minor/etc.) attached to base sets (pitch class sets). The base set and the shape set are usually given the structure of a group, more particularly a cyclic group. In a…

In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.

We derive the algebraic relations of alternating and non-alternating finite harmonic sums up to the sums of depth~6. All relations for the sums up to weight~6 are given in explicit form. These relations depend on the structure of the index…

We study a summability method called almost convergence for bounded measurable functions defined on a locally compact abelian group. We define almost convergence using topologically invariant means and exhibit two different kinds of…

In the present paper, we develop geometric analytic techniques on Cayley graphs of finitely generated abelian groups to study the polynomial growth harmonic functions. We develop a geometric analytic proof of the classical Heilbronn theorem…

We define a class of spaces on which one may generalise the notion of compactness following motivating examples from higher-dimensional number theory. We establish analogues of several well-known topological results (such as Tychonoff's…

Classical harmonic analysis says that the spaces of homogeneous harmonic polynomials (solutions of Laplace equation) are irreducible modules of the corresponding orthogonal Lie group (algebra) and the whole polynomial algebra is a free…

Harmonic maps are nonlinear extensions of harmonic functions. They are critical points of natural energy functionals between Riemannian manifolds. Such type of problems appear in Physics, Geometry of Finance and the study of regularity and…

In this paper we study singular integrals on small (that is, measure zero and lower than full dimensional) subsets of metric groups. The main examples of the groups we have in mind are Euclidean spaces and Heisenberg groups. In addition to…

Recent advances in our understanding of higher derived limits carry multiple implications in the fields of condensed and pyknotic mathematics, as well as for the study of strong homology. These implications are thematically diverse,…

In this paper, we propose an approach to controller synthesis for a class of constrained nonlinear systems. It is based on the use of a hybridization, that is a hybrid abstraction of the nonlinear dynamics. This abstraction is defined on a…

We consider a class of non-locally compact groups on which one may define a left-invariant, finitely additive measure taking values in some finitely generated extension of the field $\mathbb{R}$ of real numbers. In particular, we recover…