Cocycles of continuous iteration semigroups

• Autorzy: Guzik G. , Jarczyk W. , Matkowski J.
• Języki publikacji: EN

Abstrakty

EN

We give the form of all continuous cocycles of continuous iteration semigroups, mapping the product of the positive half-line and an interval into a topological group.

Słowa kluczowe

EN

cocycle; iteration semigroup; triangular equation

PL

kocykl; półgrupa iteracji

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2003
• Tom: Vol. 51, no 2
• Strony: 185--197
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Guzik G.

• Faculty of Applied Mathematics, Academy of Mining and Metalurgy, Mickiewicza 30, 30-059 Kraków, Poland

autor

Jarczyk W.

• Institute of Mathematics, University of Zielona Góra, Szafrana 4a, 65-516 Zielona Góra, Poland
• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

autor

Matkowski J.

• Institute of Mathematics, University of Zielona Góra, Szafrana 4a, 65-516 Zielona Góra, Poland
• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

Bibliografia

• [1] J. Aczél, Lectures on functional equations and their applications, Academic Press, New York-London 1966.
• [2] J. Aczél, B. Forte, C. T. Ng, On a triangular functional equation and some applications, in particular to the generalized theory of information, Aequationes Math., 11 (1974) 11-30.
• [3] W. Arendt, Characterizations of positive semigroups on C0(X), in: One parameter semigroups of positive operators, Lecture Notes in Math., 1184 Springer, Berlin-New York (1986) 122-162.
• [4] G. Guzik, On embedding of a linear functional equation, Rocznik Nauk. Dyd. WSP w Krakowie, 207 (1999) 23-33.
• [5] G. Guzik, On continuity of measurable cocycles, J. Appl. Anal., 6 (2000) 295-302.
• [6] M. Hmissi, Sur l’équation fonctionnelle des cocycles d’un système semidynamique, in: European Conference on Iteration Theory, Batschuns 1989, World Scientific, Singapore 1991, 149-156.
• [7] M. Hmissi, Sur les solutions globales de l’équation des cocycles, Aequationes Math., 45 (1993) 195-206.
• [8] Z. Moszner, Solution générale de l’équation F(x, y)F(y, z) = F(x, z) pour x ≤ y ≤ z, C.R. Acad. Sc. Paris, 261 (1965) 28.
• [9] Z. Moszner, Structure de l’automate plein, réduit et inversible, Aequationes Math., 9 (1973) 46-59.
• [10] Z. Moszner, Sur le prolongement covariant d’une équation linéaire par rapport au groupe d’itération, Sitzungsber. Abt. II, 207 (1998) 173-182.
• [11] Z. Moszner, Les équations et les inégalités liées à l’équation de translation, Opuscula Math., 19 (1999) 19-43.
• [12] L. Reich, 24 Remark, in: The Thirty-Fifth International Symposium on Functional Equations, Graz-Mariatrost, Austria, (September 7-14, 1997) Aequationes Math., 55 (1998) 311-312.
• [13] H. Totoki, Time changes of flows, Mem. Fac. Sci. Kyushu Univ., A20 (1966) 26-55.
• [14] E. Vesentini, Semiflows and semigroups, Rend. Mat. Accad. Lincei, 7 (9) (1996) 75-82.
• [15] M. C. Zdun, Continuous and differentiable iteration semigroups, Pra. Nauk. Uniw. Śl. Katow., 308 (1979).