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$\mathcal{P}$-adic system; differentiation basis; variational measure; Ward Theorem
In this paper we prove that each differentiation basis associated with a $\mathcal{P}$-adic path system defined by a bounded sequence satisfies the Ward Theorem.
[1] Bongiorno, B., Di Piazza, L., Skvortsov, A. V.: The essential variation of a function and some convergence theorems. Anal. Math. 22 (1996), 3–12. DOI 10.1007/BF02342334 | MR 1384345
[2] Bongiorno, B., Di Piazza, L., Skvortsov, A. V.: On variational measures related to some bases. J. Math. Anal. Appl. 250 (2000), 533–547. DOI 10.1006/jmaa.2000.6983 | MR 1786079
[3] Bongiorno, B., Di Piazza, L., Skvortsov, A. V.: On dyadic integrals and some other integrals associated with local systems. J. Math. Anal. Appl. 271 (2002), 506–524. DOI 10.1016/S0022-247X(02)00146-4 | MR 1923649
[4] Fu, Sh.: Path Integral: An inversion of path derivatives. Real Anal. Exch. 20 (1994–95), 340–346. DOI 10.2307/44152493 | MR 1313697
[5] Golubov, B., Efimov, A., Skvortsov, A. V.: Walsh Series and Transforms: Theory and Applications. Nauka, Moskva, 1987. (Russian) MR 0925004
[6] Koroleva, M.: Generalized integrals in the theory of series with respect to multiplicative systems and Haar type system. Thesis, Moscow State University.
[7] Saks, S.: Theory of Integral. Dover, New York, 1937. MR 0167578
[8] Thomson, B. S.: Some propriety of variational measure. Real Anal. Exch. 24 (1998–99), 845–854. DOI 10.2307/44153004 | MR 1704758
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