Previous |  Up |  Next

Article

Keywords:
local system; ${\mathcal{P}}$-adic system; differentiation basis; variational measure; Ward property
Summary:

References:
[1] G. N. Agaev, N. Ya. Vilenkin, G. M. Dzhafarli and A. I. Rubinshtein: Multiplicative systems of functions and harmonic analysis on zero-dimensional groups. Baku (1981). (Russian) MR 0679132
[2] E. S. Bajgogin: On a dyadic Perron integral. Vestnik Moskov. Univ. Ser. I Mat. Mekh. 48 (1993), 25–28. MR 1274657
[3] B. Bongiorno, L. Di Piazza and D. Preiss: Infinite variation and derivatives in ${R}^n$. J. Math. Anal. Appl. 224 (1998), 22–33. MR 1632942
[4] B. Bongiorno, L. Di Piazza and V. A. Skvortsov: A new full descriptive characterization of the Denjoy-Perron integral. Real Anal. Exchange. 21 (1995–96), 656–663. MR 1407278
[5] B. Bongiorno, L. Di Piazza and V. A. Skvortsov: On variational measures related to some bases. J. Math. Anal. Appl. 250 (2000), 533–547. MR 1786079
[6] B. Bongiorno, L. Di Piazza and V. A. Skvortsov: On dyadic integrals and some other integrals associated with local systems. J. Math. Anal. Appl. 271 (2002), 506–524. MR 1923649
[7] B. Bongiorno, L. Di Piazza and V. A. Skvortsov: The Ward property for a ${\mathcal{P}}$-adic basis and the ${\mathcal{P}}$-adic integral. J. Math. Anal. Appl. 285 (2003), 578–592. MR 2005142
[8] B. Bongiorno, W. Pfeffer and B. S. Thomson: A full descriptive definition of the gage integral. Canad. Math. Bull. 39 (1996), 390–401. MR 1426684
[9] Z. Buczolich and W. Pfeffer: When absolutely continuous implies $\sigma $-finite. Acad. Roy. Belg. Bull. Cl. Sci. 8 (1997), 155–160. MR 1625113
[10] Z. Buczolich and W. Pfeffer: On absolute continuity. J. Math. Anal. Appl. 222 (1998), 64–78. MR 1623859
[11] W. Cai-shi and D. Chuan-Song: An integral involving Thomson’s local systems. Real Anal. Exchange 19 (1993/94), 248–253. MR 1268851
[12] L. Di Piazza: Variational measures in the theory of the integration in $R^m$. Czechoslovak Math. J. 51 (2001), 95–110. MR 1814635
[13] V. Ene: Real functions-Current Topics. Lecture Notes in Math., Vol. 1603, Springer-Verlag, 1995. MR 1369575 | Zbl 0866.26002
[14] V. Ene: Thomson’s variational measures. Real Anal. Exchange 24 (1998/99), 523–565. MR 1704732
[15] Sh. Fu: Path integral: an inversion of path derivatives. Real Anal. Exchange 20 (1994–95), 340–346. MR 1313697
[16] B. Golubov, A. Efimov and V. A. Skvortsov: Walsh series and transforms-Theory and applications. Kluwer Academic Publishers, 1991. MR 1155844
[17] R. A. Gordon: The inversion of approximate and dyadic derivatives using an extension of the Henstock integral. Real Anal. Exchange 16 (1990–91), 154–168. MR 1087481
[18] R. A. Gordon: The Integrals of Lebesgue, Denjoy, Perron, and Henstock. Graduate Studies in Mathematics., Vol. 4, AMS, Providence, 1994. MR 1288751 | Zbl 0807.26004
[19] J. Jarník and J. Kurzweil: Perron-type integration on $n$-dimensional intervals and its properties. Czechoslovak Math. J. 45 (1995), 79–106. MR 1314532
[20] J. Kurzweil and J. Jarník: Differentiability and integrability in $n$-dimension with respect to $\alpha $-regular intervals. Results Math. 21 (1992), 138–151. MR 1146639
[21] Tuo-Yeong Lee: A full descriptive definition of the Henstok-Kurzwail integral in the Euclidean space. Proceedings of London Math. Society 87 (2003), 677–700. MR 2005879
[22] K. M. Ostaszewski: Henstock integration in the plane. Memoirs of the AMS, Providence Vol. 353, 1986. MR 0856159 | Zbl 0596.26005
[23] W. F. Pfeffer: The Riemann Approach to Integration. Cambridge Univ. Press, Cambridge, 1993. MR 1268404 | Zbl 0804.26005
[24] W. F. Pfeffer: The Lebesgue and Denjoy-Perron integrals from a descriptive point of view. Ricerche di Matematica Vol. 48, 1999. MR 1760817 | Zbl 0951.26005
[25] S. Saks: Theory of the integral. Dover, New York, 1964. MR 0167578
[26] V. A. Skvortsov: Variation and variational measures in integration theory and some applications. J. Math. Sci. (New York) 91 (1998), 3293–3322. MR 1657287
[27] V. A. Skvortsov and M. P. Koroleva: Series in multiplicative systems convergent to Denjoy-integrable functions. Mat. sb. 186 (1995), 129–150. MR 1376095
[28] V. A. Skvortsov and F. Tulone: Generalized Henstock integrals in the theory of series with respect to multiplicative system. Vestnik Moskov. Gos. Univ. Ser. Mat. Mekh. 4 (2004), 7–11. MR 2082794
[29] V. A. Skvortsov and Yu. A. Zherebyov: On classes of functions generating absolutely continuous variational measures. Real. Anal. Exchange 30 (2004–2005), 361–372. MR 2127542
[30] V. A. Skvortsov and Yu. A. Zherebyov: On Radon-Nikodim derivative for the variational measure constructed by dyadic basis. Vestnik Moskov. Univ. Ser. I Mat. Mekh. (2004), 6–12 (Engl. transl. Moscow Univ. Math. Bull. 59 (2004), 5–11). MR 2129296
[31] B. S. Thomson: Real functions. Lecture Notes in Math., Vol. 1170, Springer-Verlag. 1985. MR 0818744
[32] B. S. Thomson: Derivation bases on the real line. Real Anal. Exchange 8 (1982/83), 67–207 and 278–442.
[33] B. S. Thomson: Some property of variational measures. Real Anal. Exchange 24 (1998/99), 845–853. MR 1704758
[34] F. Tulone: On the Ward Theorem for ${\mathcal{P}}$-adic path bases associated with a bounded sequence ${\mathcal{P}}$. Math. Bohem. 129 (2004), 313–323. MR 2092717
Partner of
EuDML logo