Functions of bounded variations on compact subsets of C

• Autorzy: Gimenez J. , Merentes N. , Vivas M.

Identyfikatory

DOI

10.14708/cm.v54i1.757

• Języki publikacji: EN

Abstrakty

EN

In this paper we introduce the concept of bounded variation for functions defined on compact subsets of the complex plane C, based on the notion of variation along a curve as defined by Ashton and Doust; We describe in detail the space so generated and show that it can be equipped, in a natural way, with the structure of a Banach algebra. We also present a necessary condition for a composition operator C_φ to act between two such spaces.

Słowa kluczowe

EN

functions of bounded variation; variation along a curve; composition operator

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2014
• Tom: Vol 54, No. 1
• Strony: 3--19
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Gimenez J.

• Departamento de Matemáticas, Universidad de Los Andes Mérida, Venezuela

autor

Merentes N.

• Escuela de Matemáticas, Universidad Central de Venezuela Caracas, Venezuela

autor

Vivas M.

• Departamento de Matemáticas, Universidad Centroccidental Lisandro Alvarado Barquisimeto, Venezuela

Bibliografia

• [1] A. Acosta, W. Aziz, J. Matkowski and N. Merentes, Uniformly continuous composition operator in the space of '-Variation functions in the sense of Riesz, Fasc. Math. 43 (2010), 5-11.
• [2] B. Ashton and Doust, I., Functions of bounded variation on compact subsets of the plane, Studia Math., 169 (2005), 163-188.
• [3] J. Appell and P.P. Zabrejko, Nonlinear superposition operator, Cambridge University Press, New York, 1990.
• [4] M. Chaika and D.Waterman, On the invariance of certain clasees of functions under composition, Proc. Amer. Math. Soc. 43 (1974), 345-348.
• [5] J. Conway, Functions of One Complex Variable I (Graduate Texts in Mathematics 11), Springer-Verlag (1978), ISBN 0-387-90328-3.
• [6] C. Jordan, Sur la série de Fourier, C. R. Acad. Sci. Paris, 2 (1881), 228-230.
• [7] J. Matkowski, A. Matkowska and N. Merentes, Remark on globally Lipschitzian composition operators, Demonstratio Math. 4 27 (1995) 1, 171-175.
• [8] J. Matkowski, On Nemytskij operators, Math. Japonica 33 (1988) 1, 81-86.
• [9] N. Merentes and S. Rivas, El operador de composición en espacios de funciones con algun tipo de variación acotada, IX Escuela Venezolana de Matem´aticas, Facultad de Ciencias-ULA, Mérida- Venezuela, 1996.
• [10] E. Schröeder, ¨ Uber Iteratierte Funcktionen, Math. Anal. 3 (1971), 296-322.
• [11] R. Singh and J. Manhas Composition Operators on Function Spaces, North Holland Math. Studies 179, Amsterdam, 1993.