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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.
Wydawca
Czasopismo
Rocznik
Tom
Strony
23--33
Opis fizyczny
Bibliogr. 10 poz.
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autor
autor
autor
- Universidad Nacional Abierta Centro Local Lara (Barquisimeto), Venezuela, tomasereu@gmail.com
Bibliografia
- [1] V. V. Chistyakov, Om mappings of bounded Variation ,Y. Dyn. Control Syst. 3 (1997), 261-289.
- [2] Y. T. Medvediev, A generalization of certain theorem of Riesz, Uspekhi Mat. Nauk 6 (1953), 115-118.
- [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.
- [4] J. Musielak and W. Orlicz, On generalized variations (i), Stuia Mathematica, T. XVIIL (1959), 11-41.
- [5] F. Riesz, Untersuchugen über Systeme Integrierberer Funktionen, Math. Analen 69 (1910), 449-497.
- [6] J. L. Sánchez, A generalization of functions with bounded variation in the Schramm sense, Dep. Math, Central Univ. Venezuela, Caracas, 2008.
- [7] M. Schramm, Funtions of φ-Bounded Variation and Riemann-Stieltjes integration, Transaction Amer. Math. Soc. 267 (1985), 49 - 63.
- [8] C. Jordan, Sur la Série de Fourier, C. R. Acad. Sci. Paris 2 (1881), 228-230.
- [9] N. Wiener, The quadratic variation of function and its fourier coefficients, Massachusett J. Math. 3 (1924), 72-94.
- [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.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0011-0075