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Characterization of functions whose forward differences are exponential polynomials

J. M. Almira (2017)

Commentationes Mathematicae Universitatis Carolinae

Given ${h_{1}, \dots, h_{t}}$ a finite subset of $ℝ^{d}$ , we study the continuous complex valued functions and the Schwartz complex valued distributions $f$ defined on $ℝ^{d}$ with the property that the forward differences $Δ_{h_{k}}^{m_{k}} f$ are (in distributional sense) continuous exponential polynomials for some natural numbers $m_{1}, \dots, m_{t}$ .

Christensen measurable solutions of generalized Cauchy functional equations.

Zbigniew Gajda (1986)

Aequationes mathematicae

Christensen measurable solutions of generalized Cauchy functional equations. (Short Communications).

Zbigniew Gajda (1986)

Aequationes mathematicae

Commutativity of set-valued cosine families

Andrzej Smajdor, Wilhelmina Smajdor (2014)

Open Mathematics

Let K be a closed convex cone with nonempty interior in a real Banach space and let cc(K) denote the family of all nonempty convex compact subsets of K. If F t: t ≥ 0 is a regular cosine family of continuous additive set-valued functions F t: K → cc(K) such that x ∈ F t(x) for t ≥ 0 and x ∈ K, then $F_{t} \circ F_{s} (x) = F_{s} \circ F_{t} (x) f o r s, t ⩾ 0 a n d x \in K$ .

Complementary permutations for abelian groups.

J.H.B. Kemperman, Teunis J. Ott (1994)

Aequationes mathematicae

Complementary permutations for abelian groups. (Summary).

J.H.B. Kemperman, Teunis J. Ott (1994)

Aequationes mathematicae

Concerning functional equations of the generalized Bol-Moufang type.

D.A. Robinson (1976)

Aequationes mathematicae

Conditional function equations and orthogonal additivity.

Jürg Rätz, Luigi Paganoni (1995)

Aequationes mathematicae

Constructing means on certain continua and functional equations.

John A. Baker, B.E. Wilder (1983)

Aequationes mathematicae

Constructing means on certain continua and functional equations. (Short Communication).

John A. Baker, B.E. Wilder (1983)

Aequationes mathematicae

Convergence of sequences of iterates of random-valued vector functions

Rafał Kapica (2003)

Colloquium Mathematicae

Given a probability space (Ω,, P) and a closed subset X of a Banach lattice, we consider functions f: X × Ω → X and their iterates $f ⁿ : X \times Ω^{ℕ} \to X$ defined by f¹(x,ω) = f(x,ω₁), $f^{n + 1} (x, ω) = f (f ⁿ (x, ω), ω_{n + 1})$ , and obtain theorems on the convergence (a.s. and in L¹) of the sequence (fⁿ(x,·)).

Correction to "On a functional equation arising from hyperbolic geometry", Volume 21 (1980), 113-116.

Walter Benz (1981)

Aequationes mathematicae

Cyclic complex vector functional equations.

Risteski, Ice B., Trenčevski, Kostadin G., Covachev, Valéry C. (2000)

APPS. Applied Sciences

D'Alembert's equation and spherical functions.

Henrik Stetkaer (1994)

Aequationes mathematicae

D'Alembert's functional equation on groups

Henrik Stetkær (2013)

Banach Center Publications

Given a (not necessarily unitary) character μ:G → (ℂ∖0,·) of a group G we find the solutions g: G → ℂ of the following version of d’Alembert’s functional equation $g (x y) + μ (y) g (x y^{- 1}) = 2 g (x) g (y)$ , x,y ∈ G. (*) The classical equation is the case of μ = 1 and G = ℝ. The non-zero solutions of (*) are the normalized traces of certain representations of G on ℂ². Davison proved this via his work [20] on the pre-d’Alembert functional equation on monoids. The present paper presents a detailed exposition of these results working directly...

D'Alembert's functional equation on restricted domains.

Margherita Fochi (1996)

Aequationes mathematicae

Der Hauptsatz über Iteration im Ring der formalen Potenzreihen.

Günther H. Mehring (1987)

Aequationes mathematicae

Determinant criteria of solvability

V. S. Kalnitsky (2013)

Banach Center Publications

In the paper [3] the determinant criterion of solvability for the Kuczma equation [4] was given. This criterion appeared in the natural way as barycenter of some mass system. It turned out that determinants do appear in many different situations as solvability criteria. The present article is aimed to review the mostly classical results in the theory of functional equations from this point of view. We begin with classical results of the linear functional equations and the determinant equations solved...

Differentiable solutions of equations involving iterated functional series.

Song, Wei (2008)

Abstract and Applied Analysis

Discretely normed Abelian groups.

Frank Zorzitto (1985)

Aequationes mathematicae

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