Related papers: Intrinsic entropy for generalized quasimetric semi…

This (quasi-)survey addresses the quasi-isometry classification of locally compact groups, with an emphasis on amenable hyperbolic locally compact groups. This encompasses the problem of quasi-isometry classification of homogeneous…

In this article, we introduce an extrinsic approach to the notion of semi-direct product, an intrinsic one (namely inside the category Gp of group itself) having been already done elsewhere. This will led us to focus our attention on two…

We propose a functional framework of fractional Sobolev spaces for a class of ultra-parabolic Kolmogorov type operators satisfying the weak H\"ormander condition. We characterize these spaces as real interpolation of natural order intrinic…

In any static spacetime the quasilocal Tolman mass contained within a volume can be reduced to a Gauss-like surface integral involving the flux of a suitably defined generalized surface gravity. By introducing some basic thermodynamics, and…

In this note, we introduce a natural notion of intrinsic Hopf-Lax semigroup in the context of the so-called intrinsically Lipschitz sections. The main aims are to prove the link between the intrinsic Hopf-Lax semigroup and the intrinsic…

A general result by Jackson (Flat algebras and the translation of universal Horn logic to equational logic, J. Symb. Log. 73(1) (2008) 90--128) implies that the lattice of all quasivarieties of groups of exponent dividing $n$ embeds into…

In this paper we study the embedding problem of an operator into a strongly continuous semigroup. We obtain characterizations for some classes of operators, namely composition operators and analytic Toeplitz operators on the Hardy space…

The paper presents variational formulae for entropy-like functionals, including Segal and R\'enyi entropies, for normal states on semifinite von Neumann algebras. The considered functionals are of the form $\tau(f(h))$ where $\tau$ is a…

We study self-adjoint semigroups of partial isometries on a Hilbert space. These semigroups coincide precisely with faithful representations of abstract inverse semigroups. Groups of unitary operators are specialized examples of…

We define a new notion of entropy for operators on Fock spaces and positive definite multi-Toeplitz kernels on free semigroups. This is studied in connection with factorization theorems for (multi-Toeplitz, multi-analytic, etc.) operators…

We study the homotopy type of the space $E(L)$ of unparametrised embeddings of a split link $L=L_1\sqcup \ldots \sqcup L_n$ in $\mathbb{R}^3$. Our main result is a simple description of the fundamental group, or motion group, of $E(L)$, and…

This paper develops a formalism of endoscopy for the metaplectic group. We define the notions of stable conjugacy, elliptic endoscopic groups, correspondence of semisimple geometric conjugacy classes and the transfer factors in this…

We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…

The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are…

Based on the well-established theory of discrete conjugate nets in discrete differential geometry, we propose and examine discrete analogues of important objects and notions in the theory of semi-Hamiltonian systems of hydrodynamic type. In…

We characterize injective objects, injective hulls and essential embeddings in the category of symmetric categories enriched in a small, integral and involutive quantaloid. In particular, injective partial metric spaces are precisely…

In order to enlarge the present arsenal of semiclassical toools we explicitly obtain here the Husimi distributions and Wehrl entropy within the context of deformed algebras built up on the basis of a new family of q-deformed coherent…

The automorphism groups of integral Lorentzian lattices act by isometries on hyperbolic space with finite covolume. In the case of reflective integral lattices, the automorphism groups are commensurable to arithmetic hyperbolic reflection…

It has been shown that defining gravitational entanglement entropies relative to quantum reference frames (QRFs) intrinsically regularizes them. Here, we demonstrate that such relational definitions also have an advantage in lattice gauge…

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…