Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

ON DIVIDED DIFFERENCE OPERATORS IN FUNCTION ALGEBRAS

ON DIVIDED DIFFERENCE OPERATORS IN FUNCTION ALGEBRAS DEMONSTRATIO MATHEMATICAVol. XLINo 22008Piotr MultarzyñskiON DIVIDED DIFFERENCE OPERATORSIN FUNCTION ALGEBRASAbstract. In this paper we study divided difference operators of any order actingin function algebras. In the definition of difference quotient operators we use a tensionstructure defined on the set of points on which depend the functions of the algebras considered. In the paper we mention the oportunity for partial difference quotient operatorsas well as for some purely algebraic definition of divided difference operators in terms ofthe suitable Leibniz product rules.1. IntroductionDivided difference operators are commonly used in numerical analysis [1].Moreover, difference quotient operators provide simple characterizations ofdifferentiability properties of functions [2]. However, in the usual case of adifference quotient operator the points must be of algebraic nature, sincethe inverse of their difference is used explicitely in the corresponding definition. In this paper we study difference quotient operators for real valuedfunctions defined on an arbitrary set of points. Therefore we introduce theconcept of a tension structure specifying an algebraic substitute of a difference between the points. Our main concentration in the present paper isfocused on the simplest case of a tension structure determined by a singletension function but in Section 5 we announce the extended framework, withmany independent tension functions http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ON DIVIDED DIFFERENCE OPERATORS IN FUNCTION ALGEBRAS

Multarzyński, Piotr
Demonstratio Mathematica , Volume 41 (2): 18 – Apr 1, 2008
Download PDF
18 pages

Loading next page...
 
/lp/de-gruyter/on-divided-difference-operators-in-function-algebras-dwASDaiirX

References (3)

Publisher
de Gruyter
Copyright
© by Piotr Multarzyński
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2008-0205
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XLINo 22008Piotr MultarzyñskiON DIVIDED DIFFERENCE OPERATORSIN FUNCTION ALGEBRASAbstract. In this paper we study divided difference operators of any order actingin function algebras. In the definition of difference quotient operators we use a tensionstructure defined on the set of points on which depend the functions of the algebras considered. In the paper we mention the oportunity for partial difference quotient operatorsas well as for some purely algebraic definition of divided difference operators in terms ofthe suitable Leibniz product rules.1. IntroductionDivided difference operators are commonly used in numerical analysis [1].Moreover, difference quotient operators provide simple characterizations ofdifferentiability properties of functions [2]. However, in the usual case of adifference quotient operator the points must be of algebraic nature, sincethe inverse of their difference is used explicitely in the corresponding definition. In this paper we study difference quotient operators for real valuedfunctions defined on an arbitrary set of points. Therefore we introduce theconcept of a tension structure specifying an algebraic substitute of a difference between the points. Our main concentration in the present paper isfocused on the simplest case of a tension structure determined by a singletension function but in Section 5 we announce the extended framework, withmany independent tension functions

Journal

Demonstratio Mathematica – de Gruyter

Published: Apr 1, 2008

There are no references for this article.