Some remarks on the algebra of functions of two variables with bounded total Φ-variation in Schramm sense

• Autorzy: Ereu T. , Merentes N. , Sánchez J-L.
• Języki publikacji: EN

Abstrakty

EN

This paper is devoted to discuss some generalizations of the bounded total Φ-variation in the sense of Schramm. This concept was defined by W. Schramm for functions of one real variable. In the paper we generalize the concept in question for the case of functions of of two variables defined on certain rectangle in the plane. The main result obtained in the paper asserts that the set of all functions having bounded total Φ-variation in Schramm sense has the structure of a Banach algebra.

Słowa kluczowe

EN

Bounded variation in the sense of Wiener; bounded total variation in the sense of Schramm; function of two variable; Banach algebra

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2010
• Tom: Vol. 50, [Z] 1
• Strony: 23--33
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Ereu T.

autor

Merentes N.

autor

Sánchez J-L.

• Universidad Nacional Abierta Centro Local Lara (Barquisimeto), Venezuela,

Bibliografia

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• [3] N. Merentes and S. Rivas, El Operador de Composición en Espacios de Funciones con algun tipo de Variación Acotada, p. 256, Facultad Ciencias-ULA, M´erida-Venezuela, 1996.
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• [6] J. L. Sánchez, A generalization of functions with bounded variation in the Schramm sense, Dep. Math, Central Univ. Venezuela, Caracas, 2008.
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• [10] L. C. Young, Sur une g´en´eralisation de la notion de variation de Pussance Pi´eme au Sens de n. wiener et sur la Convergence des Séries de Fourier, C. R. Acad. Sci. Par´is, Ser A-B (1937), no. 240, 470-472.