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In this paper, we construct a partial group \(\mathcal{P}(F)\) that represents the "partial symmetry" inherent in a subset \(F\) of \(d\)-dimensional Euclidean space. In cases where \(F\) is not connected, \(\mathcal{P}(F)\) captures more…
Let $\mathcal S$ be a semigroup of partial isometries acting on a complex, infinite-dimensional, separable Hilbert space. In this paper we seek criteria which will guarantee that the selfadjoint semigroup $\mathcal T$ generated by $\mathcal…
Given $m\in \mathbb{N},$ a numerical semigroup with multiplicity $m$ is called packed numerical semigroup if its minimal generating set is included in $\{m,m+1,\ldots, 2m-1\}.$ In this work, packed numerical semigroups are used to built the…
Quasidiagonal operators on a Hilbert space are a large and important class (containing all self-adjoint operators for instance). They are also perfectly suited for study via the finite section method (a particular Galerkin method). Indeed,…
The extended weight semigroup of a homogeneous space G/H of a connected semisimple algebraic group G characterizes the spectra of the representations of G on the spaces of regular sections of homogeneous linear bundles over G/H, including…
We express total set of rational Gromov-Witten invariants of projective spaces via periods of variations of semi-infinite Hodge structure associated with their mirror partners.
A unitary representation of a, possibly infinite dimensional, Lie group G is called semi-bounded if the corresponding operators id\pi(x) from the derived representations are uniformly bounded from above on some non-empty open subset of the…
We define a numerical quasi-isometry invariant of a finitely generated group, whose values parametrize the difference between the group being uniformly embeddable in a Hilbert space and the reduced C*-algebra of the group being exact.
Semiuniform semigroups provide a natural setting for the convolution of generalized finite measures on semigroups. A semiuniform semigroup is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the…
In this article we prove some previously announced results about metric ultraproducts of finite simple groups. We show that any non-discrete metric ultraproduct of alternating or special linear groups is a geodesic metric space. For more…
For numerical semigroups with three generators, we study the asymptotic behavior of weighted factorization lengths, that is, linear functionals of the coefficients in the factorizations of semigroup elements. This work generalizes many…
In this paper, we study a special class of quasi-homomorphisms, i.e. quasi-retractions from a group to its subgroups. We first give some algebraic and geometric properties of quasi-retracts and then propose a theory of quasi-split short…
In this note we introduce the concept of a semi-bounded unitary representations of an infinite-dimensional Lie group $G$. Semi-boundedness is defined in terms of the corresponding momentum set in the dual $\g'$ of the Lie algebra $\g$ of…
In this paper, structural properties of lower semi-frames in separable Hilbert spaces are explored with a focus on transformations under linear operators (may be unbounded). Also, the direct sum of lower semi-frames, providing necessary and…
A quasi-automatic semigroup is defined by a finite set of generators, a rational (regular) set of representatives, such that if a is a generator or neutral, then the graph of right multiplication by a on the set of representatives is a…
In a series of previous papers, we initiated a systematic study of semihypergroups and had a thorough discussion on certain analytic and algebraic aspects associated to this class of objects. In particular, we introduced the notion of…
In this paper we study fixed point properties for semitopological semigroup of nonexpansive mappings on a bounded closed convex subset of a Banach space. We also study a Schauder fixed point property for a semitopological semigroup of…
A numerical semigroup is a subset of N containing 0, closed under addition and with finite complement in N. An important example of numerical semigroup is given by the Weierstrass semigroup at one point of a curve. In the theory of…
In the paper the notion of a star partial homeomorphism of a finite dimensional Euclidean space $\mathbb{R}^n$ is introduced. We describe the structure of the semigroup $\mathbf{PStH}_{\mathbb{R}^n}$ of star partial homeomorphisms of the…
We construct normed spaces of real-valued functions with controlled growth on possibly infinite-dimensional state spaces such that semigroups of positive, bounded operators $(P_t)_{t\ge 0}$ thereon with $\lim_{t\to 0+}P_t f(x)=f(x)$ are in…