相关论文: Notes on normed algebras, 3

In this paper, we establish a demi-distributions theory which develops the usual distribution theory, in particular, we show that many conclusions as differentiations, Fourier transforms and convolutions can be generalized to the…

Let $(Q,\sigma)$ be a symmetric quiver, where $Q=(Q_0,Q_1)$ is a finite quiver without oriented cycles and $\sigma$ is a contravariant involution on $Q_0\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear form $<,>$ on…

We consider the notion of a confluent spherical function on a connected semisimple Lie group, $G,$ with finite center and of real rank $1,$ and discuss the properties and relationship of its algebra with the well-known Schwartz algebra of…

In these notes we will survey recent results on various finitary approximation properties of infinite groups. We will discuss various restrictions on groups that are approximated for example by finite solvable groups or finite-dimensional…

We study quivers with relations given by non-commutative analogs of Jacobian ideals in the complete path algebra. This framework allows us to give a representation-theoretic interpretation of quiver mutations at arbitrary vertices. This…

We apply recent results on semi-classical trace formulae and on Birkhoff normal forms for semi-classical Fourier integral operators to a wide range of semi-classical and high energy spectral inverse problems.

We introduce a certain class of summability methods on $L^{\infty}([1, \infty))$ which is defined by convolution in the group algebra $L^1(\mathbb{R}^{\times})$. This class contains an integral version of Ces\`{a}ro summability method and…

We explore the relationship between subgroups and the possible shifts of finite type (SFTs) that can be defined on the group. In particular, we investigate two group invariants, weak periodicity and strong periodicity, defined via symbolic…

We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is also investigated. In the special case of finite semigroups,…

We prove the precise inversion of adjunction formula for finite linear group quotients of complete intersection varieties defined by semi-invariant equations. As an application, we prove the semi-continuity of minimal log discrepancies for…

We survey the operator algebras arising as commutants modulo normed ideals of finite sets of hermitian operators and connections to perturbations of operators and noncommutative geometry.

We investigate several infinite product of cosines and find the closed form using the Fourier transform. The answers provide limiting distributions for some elementary probability experiments.

This paper contributes to the study of sets of finite intrinsic perimeter in Carnot groups. Our intent is to characterize in which groups the only sets with constant intrinsic normal are the vertical half-spaces. Our viewpoint is algebraic:…

Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…

We discuss some structural properties of finitely generated shift-invariant (FGSI) spaces and subspaces of Sobolev spaces, particularly those related to convolution and the product within these spaces. We find shift-invariant solutions in…

Necessary and sufficient conditions for finite commutative semihypergroups to be built from abelian groups of the same order are established.

The finite basis property is often connected with the finite rank property, which it entails. Many examples have been produced of finite rank varieties which are not finitely based. In this note, we establish a result on nilpotent…

We construct canonical integral transforms, analogous to the Fourier transform, that have periods six and three. The existence of such transforms is shown to arise naturally from the expectation that the Schwartz space on the real line,…

We provide a power-saving bound for certain smoothed shifted convolution sums for Fourier coefficients of Siegel cusp forms. This result is the first nontrivial estimate for a shifted convolution sum with two cusp forms on a group of higher…

A noncommutative *-algebra that generalizes the canonical commutation relations and that is covariant under the quantum groups SOq(3) or SOq(1,3) is introduced. The generating elements of this algebra are hermitean and can be identified…