On divided difference operators in function algebras

• Autorzy: Multarzyński P.
• Języki publikacji: EN

Abstrakty

EN

In this paper we study divided difference operators of any order acting in function algebras. In the definition of difference quotient operators we use a tension structure 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 operators as well as for some purely algebraic definition of divided difference operators in terms of the suitable Leibniz product rules.

Słowa kluczowe

EN

difference operator; right invertibility; Taylor formula

PL

operatory różnicowe; wzór Taylora

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 2
• Strony: 273--289
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Multarzyński P.

• Faculty of Mathematics and Information Science Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland,

Bibliografia

• [1] L. Verde-Star, Interpolation and combinatorial functions, Stud. Appl. Math. 79 (1988), 65-92.
• [2] A. Frälicher, A. Kriegel, Linear Spaces and Diferentiation Theory, Pure and Applied Mathematics, J. Wiley and Sons, Chichester, 1988.
• [3] D. Przeworska-Rolewicz, Algebraic Analysis, PWN, Warszawa/Reidel, Dordrecht, 1988.
• [4] G. Virsik, Right inverses of vector fields, J. Austral. Math. Soc. (Series A) 58 (1995) 411-420.
• [5] P. Multarzyński, On some right invertible operators in differential spaces, Demonstratio Math. Vol.XXXVII, No 4 (2004) 905-920.