Related papers: $n$-valued Coset Groups and Dynamics
We prove various estimates for the asymptotics of counting functions associated to point sets of coherent frames and Riesz sequences. The obtained results recover the necessary density conditions for coherent frames and Riesz sequences for…
We extend the notions of nonautonomous dynamics to arbitrary groups, through groupoid morphisms. This also presents a generalization of classic dynamical systems and group actions. We introduce the structure of cotranslations, as a specific…
We present an asymptotic evaluation unitary formula for large argument values existing for defined class of functions. The asymptotic evaluation is obtained using only power series expansion coefficients of a function, what is a new result…
We derive new approximate representations of the Lommel functions in terms of the Scorer function and approximate representations of the first derivative of the Lommel functions in terms of the derivative of the Scorer function. Using the…
This study delves into the exploration of the limiting shape theorem for subadditive processes on finitely generated groups with polynomial growth, commonly referred to as virtually nilpotent groups. Investigating the algebraic structures…
The isotropic harmonic oscillator in N dimensions is shown to have an underlying symmetry group O(2,1)X O(N)which implies a unique result for the energy spectrum of the system. Raising and lowering operators analogous to those of the…
In the semisimple case, we derive (asymptotic) formulas for the growth rate of the number of summands in tensor powers of the generating object in diagram/interpolation categories.
In this paper we study the asymptotic behavior of the number of summands in tensor products of finite dimensional representations of affine (semi)group (super)schemes and related objects.
We consider set of functions on Poisson manifold related by continues one-parameter group of transformations. Class of vector fields that produce involutive families of functions is investigated and relationship between these vector fields…
We point out an asymptotic formula for the power moments of the function $a(n)$, representing the number of non-isomorphic Abelian groups of order $n$. For the quadratic moment this improves an earlier result due to L. Zhang, M. L\"u and W.…
We survey several notions of Mackey functors and biset functors found in the literature and prove some old and new theorems comparing them. While little here will surprise the experts, we draw a conceptual and unified picture by making…
In this note, presented as a ``community service", followed by the PhD research of the author, we draw the relation between Casselman's theorem regarding the asymptotic behavior of matrix coefficients of reductive algebraic groups over…
The symbolic method is used to get explicit formulae for the products or powers of Bessel functions and for the relevant integrals.
We determine the possible functions that can occur, up to asymptotic equivalence, as growth functions of semigroups, hereditary languages, and algebras.
In this paper, we study connections between the structure of a group and the structure of the group (under pointwise product) of its polynomial functions.
We review novel results and investigate actions and transformations of groups and semigroups on (quantum) spaces, present dynamical systems and zeta functions arising from these spaces, actions and transformations, discuss their stochastic…
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 consider asymptotic expansions for a class of sequences of symmetric functions of many variables. Applications to classical and free probability theory are discussed.
We prove the asymptotic formulas for the transition densities of isotropic unimodal convolution semigroups of probability measures on $\mathbb{R} ^d$ under the assumption that its L\'{e}vy--Khintchine exponent varies slowly. We also derive…
General results on asymptotic expansions of Feynman diagrams in momenta and/or masses are reviewed. It is shown how they are applied for calculation of massive diagrams.