# On difference equations with variable increments.

Stochastica (1980)

• Volume: 4, Issue: 2, page 93-101
• ISSN: 0210-7821

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## Abstract

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Let X be an arbitrary Abelian group and E a Banach space. We consider the difference-operators ∆n defined by induction:(∆f)(x;y) = f(x+y) - f(x), (∆nf)(x;y1,...,yn) = (∆n-1(∆f)(.;y1)) (x;y2,...,yn)(n = 2,3,4,..., ∆1=∆, x,yi belonging to X, i = 1,2,...,n; f: X --&gt; E).Considering the difference equation (∆nf)(x;y1,y2,...,yn) = d(x;y1,y2,...,yn) with independent variable increments, the most general solution is given explicitly if d: X x Xn --&gt; E is a given bounded function. Also the most general form of bounded functions in the range of ∆n is determined.Another type of operator, designed by ∆2n is defined by(∆2f)(x;y) = f(x+2y) - 2f(x+y) + f(x),(∆2nf)(x;y1,...,yn) = (∆2n-1(∆2f)(.;y1)) (x;y2,...,yn),(n = 2,3,4,..., ∆21=∆2, x,yi belonging to X, i = 1,2,...,n) and under the same conditions as above the most general solution of the equation ∆2nf = d is established.

## How to cite

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Borelli Forti, Constanza, and Fenyö, István. "Sulle equazioni alle differenze con incrementi variabili.." Stochastica 4.2 (1980): 93-101. <http://eudml.org/doc/38830>.

@article{BorelliForti1980,
author = {Borelli Forti, Constanza, Fenyö, István},
journal = {Stochastica},
keywords = {Ecuaciones en diferencias; Incrementos variables; Banach space; difference-operators; general solution},
language = {ita},
number = {2},
pages = {93-101},
title = {Sulle equazioni alle differenze con incrementi variabili.},
url = {http://eudml.org/doc/38830},
volume = {4},
year = {1980},
}

TY - JOUR
AU - Borelli Forti, Constanza
AU - Fenyö, István
TI - Sulle equazioni alle differenze con incrementi variabili.
JO - Stochastica
PY - 1980
VL - 4
IS - 2
SP - 93
EP - 101
LA - ita
KW - Ecuaciones en diferencias; Incrementos variables; Banach space; difference-operators; general solution
UR - http://eudml.org/doc/38830
ER -

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