Related papers: Moment functions on groups
The moments of Bessel functions and Bessel-trigonometric functions play a basic role in many practical problems and numerical analysis. This paper presents a complete analysis for these moments based on the recursive relations of Bessel…
This paper introduces and develops the algebraic framework of moment polynomials, which are polynomial expressions in commuting variables and their formal mixed moments. Their positivity and optimization over probability measures supported…
We define an enumerative function F(n,k,P,m) which is a generalization of binomial coefficients. Special cases of this function are also power function, factorials, rising factorials and falling factorials. The first section of the paper is…
Frobenius built a representation theory of finite groups in the process of obtaining the irreducible factorization of the group determinant. Here, we give a generalization of Frobenius' theorem. The generalization leads to a corollary on…
Stanley introduces polynomials which help evaluate symmetric group characters and conjectures that the coefficients of the polynomials are positive. Stanley later gives a conjectured combinatorial interpretation for the coefficients of the…
In the paper, the author studies properties of three functions relating to the exponential function and the existence of partitions of unity, including accurate and explicit computation of their derivatives, analyticity, complete…
This survey provides an exposition of a suite of techniques based on the theory of polynomials, collectively referred to as polynomial methods, which have recently been applied to address several challenging problems in statistical…
We consider the problem of defining polynomials over function fields of positive characteristic. Among other results, we show that the following assertions are true. 1. Let $\G_p$ be an algebraic extension of a field of $p$ elements and…
In this short note we give a characterization of ZM-groups that uses the functions defined and studied in [3,4]. This leads to a proof of Conjecture 6 in [4].
The main purpose of this article is to present a generalization of Forelli's theorem for the functions holomorphic along a general pencil of holomorphic discs. This generalizes the main result of \cite{JKS13} and the original Forelli's…
In this article, we investigate the pointwise behaviors of functions on the Heisenberg group. We find wavelet characterizations for the global and local H\"older exponents. Then we prove some a priori upper bounds for the multifractal…
We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…
This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be…
We use double categories to obtain a single theorem characterizing certain exponentiable morphisms of small categories, topological spaces, locales, and posets.
We prove that polycyclic groups are of polynomial growth or of uniform exponential growth.
We define a modular function which is a generalization of the elliptic modular lambda function. We show this function and the modular invariant function generate the modular function field with respect to the principal congruence subgroup.…
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…
We extend to several variables an earlier result of ours, according to which an entire function of one variable of sufficiently small exponential type, having all derivatives of even order taking integer values at two points, is a…
Compounding submodular monotone (i.e. 2-alternating) set functions on a finite set preserves this property, as shown in 2010. A natural generalization to k-alternating functions was presented in 2018, however hardly readable because of page…
The aim of this paper is to establish various factorization results and then to derive estimates for linear functionals through the use of a generalized Taylor theorem. Additionally, several error bounds are established including…