Related papers: Harmonic Synthesis on Group Extensions

Two types of finite series of products of harmonic numbers involving nonnegative integer powers are evaluated, also yielding two other important harmonic number identities. The recursion formulas for these sums are derived, which are easily…

A totally symmetric set is a finite subset of a group for which any permutation of the elements can be realized by conjugation in the ambient group. Such sets are rigid under homomorphisms, and so exert a great deal of control over the…

Using the completed inductive, projective and injective tensor products of Grothendieck for locally convex topological vector spaces, we develop a systematic theory of locally convex Hopf algebras with an emphasis on Pontryagin-type…

In this paper, we address the equivalence of the analytic and probabilistic notions of harmonicity in the context of general symmetric Hunt processes on locally compact separable metric spaces. Extensions to general symmetric right…

A sequence of representations \(V_n\) of the symmetric group \(S_n\) is called representation (multiplicity) stable if, after some \(n\), the irreducible decomposition of \(V_n\) stabilizes. In particular, Church, Ellenburg and Farb (2015)…

The computation of Feynman integrals in massive higher order perturbative calculations in renormalizable Quantum Field Theories requires extensions of multiply nested harmonic sums, which can be generated as real representations by Mellin…

In this paper, we consider a control synthesis problem for a class of polynomial dynamical systems subject to bounded disturbances and with input constraints. More precisely, we aim at synthesizing at the same time a controller and an…

We continue classification of finite groups which can be used as symmetry group of the scalar sector of the four-Higgs-doublet model (4HDM). Our objective is to systematically construct non-abelian groups via the group extension procedure,…

We show that if $p \colon M \to N$ is a normal Riemannian covering, with $N$ closed, and $M$ has exponential volume growth, then there are non-constant, positive harmonic functions on $M$. This was conjectured by Lyons and Sullivan in…

Let $k$ be a field. We characterize the group schemes $G$ over $k$, not necessarily affine, such that $\mathsf{D}_{\mathrm{qc}}(B_kG)$ is compactly generated. We also describe the algebraic stacks that have finite cohomological dimension in…

We present a simple representation for analytically continued nested harmonic sums for the arbitrary complex argument. This representation can be obtained for a wide range of nested harmonic sums from a precomputed database for the pole…

We explore the relationship between convex and subharmonic functions on discrete sets. Our principal concern is to determine the setting in which a convex function is necessarily subharmonic. We initially consider the primary notions of…

In this work we establish a connection between two classical notions, unrelated so far: Harmonic functions on the one hand and absolutely monotonic functions on the other hand. We use this to prove convexity type and propagation of…

Making use of nonabelian harmonic analysis and representation theory, we solve the functional equation $$f_1(xy)+f_2(yx)+f_3(xy^{-1})+f_4(y^{-1}x)=f_5(x)f_6(y)$$ on arbitrary compact groups. The structure of its general solution is…

Infinitesimal contraction analysis, wherein global asymptotic convergence results are obtained from local dynamical properties, has proven to be a powerful tool for applications in biological, mechanical, and transportation systems. Thus…

Let $G$ and $H$ be locally compact groups and consider their associate spaces of almost periodic functions $AP(G)$ and $AP(H)$. We investigate the continuous group homomorphisms induced by isometries of $AP(G)$ into $AP(H)$. Among others,…

If $A$ and $B$ are subsets of an abelian group, their sumset is $A+B:=\{a+b:a\in A, b\in B\}$. We study sumsets in discrete abelian groups, where at least one summand has positive upper Banach density. Renling Jin proved that if $A$ and $B$…

Analytic properties of right topological groups have been extensively studied in the compact admissible case (i.e when the group has a dense topological center). This was inspired by the existence of a Haar measure on such groups. In this…

In this work, we present a compositional safety controller synthesis approach for the class of discrete-time linear control systems. Here, we leverage a state-of-the-art result on the computation of robust controlled invariant sets. To…

In this paper we generalize a result in [1], showing that an arbitrary Riemannian symmetric space can be realized as a closed submanifold of a covering group of the Lie group defining the symmetric space. Some properties of the subgroups of…