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Quasi-Invariant and Pseudo-Differentiable Measures with Values in Non-Archimedean Fields on a Non-Archimedean Banach Space

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REFERENCES

  1. I. Ya. Aref'eva, B. Dragovich, and I. V. Volovich, “On the p-adic summability of the anharmonic oscillator,” Phys. Lett., B 200, 512–514 (1988).

    Google Scholar 

  2. A. H. Bikulov and I. V. Volovich, “p-Adic Brounian motion”, Izv. Ross. Akad. Nauk, Ser. Mat., 61,No. 3, 75–90 (1997).

    Google Scholar 

  3. S. Bosch, U. Guntzer, and R. Remmert, Non-Archimedean Analysis, Springer, Berlin (1984).

    Google Scholar 

  4. V. I. Bogachev and O. G. Smolyanov, “Analytic properties of inifinite-dimensional distributions”, Usp. Mat. Nauk, 45No. 3, 3–83 (1990).

    Google Scholar 

  5. N. Bourbaki, Intégration, Livre VI. Fasc. XIII, XXI, XXIX, XXXV. Ch. 1–9, Hermann, Paris 1965, 1967, 1963, 1969).

    Google Scholar 

  6. J. P. R. Christensen. Topology and Borel Structure, North-Holland Math. Studies, No. 10, Elsevier, Amsterdam (1974).

    Google Scholar 

  7. C. Constantinescu, Spaces of Measures, Springer, Berlin (1984).

    Google Scholar 

  8. Yu. L. Dalecky and S. V. Fomin, Measures and Differential Equations in Infinite-Dimensional Spaces Kluwer Acad. Publ., Dordrecht (1991).

    Google Scholar 

  9. G. S. Djordjević and B. Dragovich. “p-Adic and adelic harmonic oscillator with a time-dependent frequency,” Theor. Math. Phys., 124No. 2, 1059–1067 (2000).

    Google Scholar 

  10. R. Engelking, General Topology [Russian translation], Mir, Moscow (1986).

    Google Scholar 

  11. H. Federer, Geometric Measure Theory, Springer, Berlin (1969).

    Google Scholar 

  12. F. R. Gantmaher, Theory of Matrices [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  13. I. M. Gelfand and N. Ya. Vilenkin, Some Applications of Harmonic Analysis. Generalized Functions, Vol. 4, Fiz.-Mat. Lit., Moscow (1961).

    Google Scholar 

  14. P. L. Henneken and A. Torta, Theory of Probability and Some of Its Applications [Russian translation], Nauka, Moscow (1974).

    Google Scholar 

  15. E. Hewitt and K. A. Ross, Abstract Harmonic Analysis Springer, Berlin (1979).

    Google Scholar 

  16. C. J. Isham and J. Milnor, In: Relativity, Groups and Topology. II, Elsevier, Amsterdam (1984), pp. 1007–1290.

    Google Scholar 

  17. Y. Jang, “Non-Archimedean quantum mechanics,” Tohoku Math. Publ., No. 10 (1998).

  18. A. Yu. Khrennikov, “Mathematical methods of non-Archimedean physics,” Usp. Mat. Nauk, 45No.4, 79–110 (1990).

    Google Scholar 

  19. A. Yu. Khrennikov and M. Endo, “Non-boundedness of p-adic Gaussian distributions,” Izv. Akad. Nauk SSSR, Ser. Mat., 56, 1104–1115 (1992).

    Google Scholar 

  20. S. V. Ludkovskii, “Measures on groups of diffeomorphisms of non-Archimedean Banach manifolds,” Usp. Mat. Nauk, 51,No. 2, 169–170 (1996).

    Google Scholar 

  21. S. V. Ludkovskii, “Non-Archimedean polyhedral expansions of ultrauniform spaces,” Fundam. Prikl. Mat., 6,No. 2, 455–475 (2000).

    Google Scholar 

  22. S. V. Ludkovskii, “Measures on diffeomorphism groups of non-Archimedean manifolds, representations of groups and their applications,” Theor. Math. Phys., 119,No. 3, 381–396 (1999).

    Google Scholar 

  23. S. V. Ludkovskii, “Quasi-invariant measures on non-Archimedean semigroups of loops,” Usp. Mat. Nauk, 53,No. 3, 203–204 (1998).

    Google Scholar 

  24. S. V. Ludkovskii, “Irreducible unitary representations of non-Archimedean groups of diffeomorphisms,” Southeast Asian Bull. Math., 22, 419–436 (1998).

    Google Scholar 

  25. S. V. Ludkovskii, “Properties of quasi-invariant measures on topological groups and associated algebras,” Ann. Math. B. Pascal, 6,No. 1, 33–45 (1999).

    Google Scholar 

  26. S. V. Ludkovskii, “Quasi-invariant measures on non-Archimedean groups and semigroups of loops and paths, their representations,” Ann. Math. Blaise Pascal, 7,No. 2, 19–53, 55–80 (2000).

    Google Scholar 

  27. S. V. Ludkovskii, “Non-Archimedean free Banach spaces,” Fund. Prikl. Mat., 1,No. 3, 979–987 (1995).

    Google Scholar 

  28. S. V. Ludkovskii, “Quasi-invariant measures on a group of diffeomorphisms of an infinite-dimensional real manifold and induced irreducible unitary representations,” Rend. dell'Istituto Mat. dell'Univ. Trieste, Nuova Ser., 31, 101–134 (1999).

    Google Scholar 

  29. A. Madrecki, “Minlos' theorem in non-Archimedean locally convex spaces,” Comment. Math. (Warsaw), 30, 101–111 (1991).

    Google Scholar 

  30. A. Madrecki, “Some negative results on existence of Sazonov topology in l-adic Frechet spaces,” Arch. Math, 56, 601–610 (1991).

    Google Scholar 

  31. A. Madrecki, “On Sazonov type topology in p-adic Banach space,” Math. Z., 188, 225–236 (1985).

    Google Scholar 

  32. A. P. Monna and T. A. Springer, “Integration non-archimedienne,” Indag. Math., 25, 634–653 (1963).

    Google Scholar 

  33. L. Narici and E. Beckenstein, Topological Vector Spaces, Marcel Dekker Inc., New York (1985).

    Google Scholar 

  34. A. C. M. van Rooij, Non-Archimedean Functional Analysis, Marcel Dekker Inc., New York (1978).

    Google Scholar 

  35. W. H. Schikhof, Ultrametric Calculus, Univ. Press, Cambridge (1984).

    Google Scholar 

  36. W. H. Schikhov, “On p-adic compact operators,” Report 8911, Dept. Math. Cath. Univ., Nijmegen, The Netherlands (1989).

    Google Scholar 

  37. W. H. Schikhof, “A Radon-Nikodym theorem for non-Archimedean integrals and absolutely continuous measures on groups,” Indag. Math., Ser. A., 33,No. 1, 78–85 (1971).

    Google Scholar 

  38. A. V. Skorohod, Integration in Hilbert Space, Springer, Berlin (1974).

    Google Scholar 

  39. O. G. Smolyanov and S. V. Fomin, “Measures on linear topological spaces,” Usp. Mat. Nauk, 31,No. 4, 3–56 (1976).

    Google Scholar 

  40. F. Topsoe, “Compactness and tightness in a space of measures with the topology of weak convergence,” Math. Scand., 34, 187–210 (1974).

    Google Scholar 

  41. F. Topsoe, “Some special results on convergent sequences of Radon measures,” Manuscr. Math., 19, 1–14 (1976).

    Google Scholar 

  42. N. N. Vahaniya, V. I. Tarieladze, and S. A. Chobanyan, Probability Distributions in Banach Spaces [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  43. V. S. Vladimirov, I. V. Volovich, and E. I. Zelenov, p-Adic Analysis and Mathematical Physics [in Russian], Nauka, Moscow (1994).

    Google Scholar 

  44. A. Weil, Basic Number Theory, Springer, Berlin (1973).

    Google Scholar 

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Ludkovsky, S.V. Quasi-Invariant and Pseudo-Differentiable Measures with Values in Non-Archimedean Fields on a Non-Archimedean Banach Space. Journal of Mathematical Sciences 122, 2949–2983 (2004). https://doi.org/10.1023/B:JOTH.0000029574.98669.a7

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