Related papers: On complete characterization of coefficients of a.…

We consider a sequence of polynomials $\{P_n\}_{n \geq 0}$ satisfying a special $R_{II}$ type recurrence relation where the zeros of $P_n$ are simple and lie on the real line. It turns out that the polynomial $P_n$, for any $n \geq 2$, is…

It is consistent that for every n >= 2, every stationary subset of omega_n consisting of ordinals of cofinality omega_k where k = 0 or k <= n-3 reflects fully in the set of ordinals of cofinality omega_{n-1}. We also show that this result…

Let $(a_n), (b_n)$ be linear recursive sequences of integers with characteristic polynomials $A(X),B(X)\in \mathbb{Z}[X]$ respectively. Assume that $A(X)$ has a dominating and simple real root $\alpha$, while $B(X)$ has a pair of conjugate…

We derive formulas for characterizing bounded orthogonally additive polynomials in two ways. Firstly, we prove that certain formulas for orthogonally additive polynomials derived in \cite{Kusa} actually characterize them. Secondly, by…

The polynomials $p_n$ orthogonal on the interval $[-1,1],$ normalized by $p_n(1)=1,$ satisfy Tur\'an's inequality if $p_n^2(x)-p_{n-1}(x)p_{n+1}(x)\ge 0$ for $n\ge 1$ and for all $x$ in the interval of orthogonality. We give a general…

A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…

This paper uses a relative of BP-cohomology to prove a theorem in characteristic p algebra. Specifically, we obtain some new necessary conditions for the existence of sums-of-squares formulas over fields of characteristic p > 2. These…

In this paper, we study the set of positive integers that characterize the universality of $m$-gonal form.

A unifying scheme of classical special functions of hypergeometric type obeying orthogonality or biorthogonality relations is described. It expands the Askey scheme of classical orthogonal polynomials and its $q$-analogue based on the…

Infinite series of the type Sum{n=1,infinity}(alpha/2)_n_2F_1(-n, b; gamma; y)/(n n!) are investigated. Closed-form sums are obtained for alpha a positive integer alpha=1,2,3, ... The limiting case of b --> infinity, after y is replaced…

F\"ur die freien orthogonalen Quantengruppen $A_o(n)$ wird ein vollst\"a ndiges Reduktionssystem angegeben und verifiziert. F\"ur den Fall $n = 2$ wird ein endlicher Automat angegeben, der s\"amtliche der Basiselemente findet. Weiterhin…

Given any $\varepsilon>0$, we construct an orthonormal system of $n_k$ uniformly bounded polynomials of degree at most $k$ on the unit sphere in $\mathbb R^{m+1}$ where $n_k$ is bigger than $1-\varepsilon$ times the dimension of the space…

We determine all affinely homogeneous models for surfaces $S^2 \subset \mathbb{R}^4$, including the simply transitive models. We employ an improved power series method of equivalence, which captures invariants at the origin, creates…

Let R and S be two irreducible root systems spanning the same vector space and having the same Weyl group W, such that S (but not necessarily R) is reduced. For each such pair (R,S) we construct a family of W-invariant orthogonal…

The conformal transformations with respect to the metric defining $o(n,\mbb{C})$ give rise to a nonhomogeneous polynomial representation of $o(n+2,\mbb{C})$. Using Shen's technique of mixed product, we generalize the above representation to…

Let H be a countable subgroup of the metrizable compact abelian group G and f:H -> T=R/Z a (not necessarily continuous) character of H. Then there exists a sequence (chi_n)_n of (continuous) characters of G such that lim_n chi_n(alpha) =…

Let $\mathcal{A}$ be a finite set of integers, and let $h\mathcal{A}$ denote the $h$-fold sumset of $\mathcal{A}$. Let $(h\mathcal{A})^{(t)}$ be subset of $h\mathcal{A}$ consisting of all integers that have at least $t$ representations as a…

We give a criterion for a group homomorphism on a valued abelian group to be surjective and to preserve spherical completeness. We apply this to give a criterion for the existence of integration on a valued differential field. Further, we…

In this article we consider orthonormal systems consisting of tensor products of splines. We show some convergence results of the corresponding orthogonal series including a.e. convergence and unconditional convergence in $L^p$ for…

A conjecture of Graham (repeated by Erd\H{o}s) asserts that for any set $A \subseteq \mathbb{F}_p \setminus \{0\}$, there is an ordering $a_1, \ldots, a_{|A|}$ of the elements of $A$ such that the partial sums $a_1, a_1+a_2, \ldots,…