17 citations · 43 across the 38 of their papers we have counts for
26 papers · 1 filter
Characterization of polynomials by their invariance properties
J. M. Amira, Ya-Qing Hu
We prove that certain classical groups serve to characterize ordinary polynomials in real variables as elements of finite-dimensional subs…
Using Aichinger's equation to characterize polynomial functions
J. M. Almira
Aichinger's equation is used to give simple proofs of several well-known characterizations of polynomial functions as solutions of certain functional equations. Concretely, we use…
On Popoviciu-Ionescu functional equation in one and several variables
J. M. Almira
We study a functional equation first proposed by T. Popoviciu in 1955. In the one-dimensional case, it was solved for the easiest case by Ionescu in 1956 and, for the general case,…
Characterization of distributions whose forward differences are exponential polynomials
J. M. Almira
Given a finite subset of , we study the continuous complex valued functions and the Schwartz complex valued distributions defined on $\mat…
Characterization of Polynomials as solutions of certain functional equations
J. M. Almira
Recently, the functional equation \[ \sum_{i=0}^mf_i(b_ix+c_iy)= \sum_{i=1}^na_i(y)v_i(x) \] with and , was studied by Alm…
On certain generalizations of the Levi-Civita and Wilson functional equations
J. M. Almira, E. V. Shulman
We study the functional equation \[ \sum_{i=1}^mf_i(b_ix+c_iy)= \sum_{k=1}^nu_k(y)v_k(x) \] with and , both in the classical con…
On polynomial functions on non-conmmutative groups
J. M. Almira, E. V. Shulman
Let be a topological group. We investigate relations between two classes of "polynomial like" continuous functions on defined, respectively, by the conditions (1) $Δ_h^{n+1…
A Montel-type theorem for mixed differences
J. M. Almira
We prove a generalization of classical Montel's theorem for the mixed differences case, for polynomials and exponential polynomial functions, in commutative setting.
On Popoviciu-Ionescu functional equation
J. M. Almira
We study a functional equation first proposed by T. Popoviciu in 1955. It was solved for the easiest case by Ionescu in 1956 and, for the general case, by Ghiorcoiasiu and Roscau,…
On Loewner's characterization of polynomials
J. M. Almira
We give a new demonstration of Loewner's characterization of polynomials, solving in the positive a conjecture proposed by Laird and McCann in 1984.
On the closure of translation-dilation invariant linear spaces of polynomials
J. M. Almira, L. Székelyhidi
Assume that a linear space of real polynomials in variables is given which is translation and dilation invariant. We show that if a sequence in this space converges pointwise t…
A dichotomy property for the graphs of monomials
J. M. Almira, Z. Boros
We prove that the graph of a discontinuous -monomial function is either connected or totally disconnected. Furthermore, the discontinuous monomial fu…
Montel-type theorems for exponential polynomials
J. M. Almira, L. Székelyhidi
In this paper we characterize local exponential monomials and polynomials on different types of Abelian groups and we prove Montel-type theorems for these function classes.
On Montel and Montel-Popoviciu theorems in several variables
A. G. Aksoy, J. M. Almira
We present an elementary proof of a general version of Montel's theorem in several variables which is based on the use of tensor product polynomial interpolation. We also prove a M…
A note on invariant subspaces and the solution of some classical functional equations
J. M. Almira, Kh. F. Abu-Helaiel
We study the continuous solutions of several classical functional equations by using the properties of the spaces of continuous functions which are invariant under some elementary…
A p-adic Montel theorem and locally polynomial functions
J. M. Almira, Kh. F. Abu-Helaiel
We prove a version of both Jacobi's and Montel's Theorems for the case of continuous functions defined over the field of -adic numbers. In particular, we prove th…
On Shapiro's lethargy theorem and some applications
A. G. Aksoy, J. M. Almira
Shapiro's lethargy theorem states that if {A_n} is any non-trivial linear approximation scheme on a Banach space X, then the sequences of errors of best approximation E(x,A_n) = \i…
A note on monomials
J. M. Almira, Kh. F. Abu-Helaiel
We study discontinuous solutions of the monomial equation . In particular, we characterize the closure of their graph, , and…
On solutions of and related equations
J. M. Almira, Kh. F. Abu-Helaiel
We study some properties of the solutions of the functional equation which was introduced in the literature by Mora, Cherruault and Ziadi in 1999, f…
A note on classical and p-adic Fréchet functional equations with restrictions
J. M. Almira
Given X,Y two Q-vector spaces, and f:X -> Y, we study under which conditions on the sets , k=1,...,s, if for all x in X and h_k in B_k, k=…
On strict inclusion relations between approximation and interpolation spaces
J. M. Almira
We study strict inclusion relations between approximation and interpolation spaces.
Shapiro's Theorem for subspaces
J. M. Almira, T. Oikhberg
In a previous paper (see arXiv:1003.3411 [math.CA]), we investigated the existence of an element x of a quasi-Banach space X whose errors of best approximation by a given approxima…
A lethargy result for real analytic functions
J. M. Almira
In this short note we prove that, if (C[a,b],{A_n}) is an approximation scheme and (A_n) satisfies de La Vallée-Poussin Theorem, there are instances of continuous functions on [a,b…
Approximation schemes satisfying Shapiro's Theorem
J. M. Almira, T. Oikhberg
An approximation scheme is a family of homogeneous subsets of a quasi-Banach space , such that , $A_n + A_n \subset A_{K(…