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Characterization of functions whose forward differences are exponential polynomials

J. M. Almira (2017)

Commentationes Mathematicae Universitatis Carolinae

Given { h 1 , , h t } a finite subset of d , we study the continuous complex valued functions and the Schwartz complex valued distributions f defined on 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 , , m t .

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 F s ( x ) = F s F t ( x ) f o r s , t 0 a n d x K .

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 : X × Ω X defined by f¹(x,ω) = f(x,ω₁), f n + 1 ( x , ω ) = f ( f ( x , ω ) , ω n + 1 ) , and obtain theorems on the convergence (a.s. and in L¹) of the sequence (fⁿ(x,·)).

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