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Tytuł artykułu

On a refinement type equation

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let (Ω, A, P) be a complete probability space. We show that the trivial function is the unique L1 -solution of the following refinement type equation [wzór] for a wide class of the given functions φ. This class contains functions of the form [wzór]
Wydawca
Rocznik
Strony
251--257
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
autor
Bibliografia
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  • [2] Baron, K., .Jarczyk, W., Random-valued functions and iterative functional equations. Aequationes Math. 67 (2004), 140-153.
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  • [4] Cavaretta. D., Dahmen, W., Micchelli. C. A. Stationary subdivision, Mem. Amer. Math. Soc. 93 (1991), 1-186.
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  • [7] Dahmen, W., Micchelli, C. A., Continuous refinement equations and subdivision. Adv. Comput. Math. 1 (1993), 1-37.
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  • [9] Daubechies. I., Lagarias, J. C., Two-scale difference equations I. Existence and global regularity of solutions, SIAM J. Math. Anal. 22 (1991), 1388-1410.
  • [10] Derfel, G., Probabilistic method for a class of functional-differential equations (in Russian), Ukrain. Mat. Zh. 41 (1989), 1322-1327, 1436, (translation in Ukrainian Math. J. 41 (1989), 1137-1141 (1990)).
  • [11] Derfel, G., Dyn, N., Levin, D., Generalized- refinement equations and. Subdivision processes, J. Approx. Theory 80 (1995), 272-297.
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  • [16] Kapica, R., Sequences of iterates of random-valued vector functions and continuous solutions of a linear functional equation of infinite order, Bull. Polish Acad. Sci. Math. 50 (2002), 447-455.
  • [17] Kapica, R., Convergence of sequences of iterates of random-valued, vector functions, Colloq. Math. 97 (2003), 1-6.
  • [18] Kapica, R., Sequences of iterates of random-valued, vector functions and solutions of related equations, Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 213 (2004), 113-118 (2005).
  • [19] Kapica, R., Morawiec, J., Probability distribution functions of the Grincevičjus series. J. Math. Anal. Appl. 342 (2008), 1380-1387.
  • [20] Kuczma, M., Normalizing factors for iterates of random valued functions, Pr. Nauk. Uniw. Śl. Katow. 6 (1975), 67-72.
  • [21] Kuratowski, K., Topology. Vol. I (translated from the French by J. Jaworowski), Academic Press, New York-London; PWN. Warsaw, 1966.
  • [22] Micchelli, C. A., Prautzsch, H., Uniform, refinement of curves, Linear Algebra Appl. 114/115 (1989), 841-870.
  • [23] Schumaker, L. L., Spline functions: Basic theory, John Wiley, New York. 1981.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD6-0006-0029
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