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Differential calculus for measures on Banach spaces

Part of the Lecture Notes in Mathematics book series (LNM,volume 644)

Keywords

  • Local Measure
  • Borel Measure
  • Differential Calculus
  • Logarithmic Derivative
  • Decomposition Property

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References

  1. J.I. Alvarez, The Riesz decomposition theorem for distributions on a Wiener space, Ph. D. Thesis, Cornell University, Ithaca, N. Y. (1973)

    Google Scholar 

  2. V. I. Averbuh, O.G. Smoljanov and S. V. Fomin, Generalized functions and differential equations in linear spaces, I. differentiable measures, Trans. Moscow Math. Soc. 24 (1971), 140–184.

    MathSciNet  Google Scholar 

  3. V. I. Averbuh, O.G. Smoljanov and S. V. Fomin, Generalized functions and differential equations in linear spaces, II. differential operators and their Fourier transforms, Trans. Moscow Math. Soc. 27 (1972), 255–270.

    MathSciNet  Google Scholar 

  4. Yu. M. Berezanskii and Yu. S. Samoilenko, Nuclear spaces of functions of infinitely many variables, Ukrainian Math. J. 25 (1973), 599–609.

    CrossRef  MathSciNet  Google Scholar 

  5. Ju. L. Daleckiľ, Infinite-dimensional elliptic operators and the corresponding parabolic equations, Russian Math. Surveys 22 (1967), no. 4, 1–53.

    CrossRef  MathSciNet  Google Scholar 

  6. Ju. L. Daleckiľ and S. V. Fomin, Generalized measures in Hilbert space and Kolmogorov's forward equation, Soviet Math. Dokl. 13 (1972), no. 4, 993–997.

    MATH  Google Scholar 

  7. D. N. Dudin, Theory of distributions on Hilbert space, Uspehi Mat. Nauk 27 (1972), no.2, 169–170.

    MathSciNet  Google Scholar 

  8. D. N. Dudin, Generalized measures or distributions on Hilbert space, Trans. Moscow Math. Soc. 28 (1973), 133–157.

    MathSciNet  MATH  Google Scholar 

  9. N. Dunford and J. T. Schwartz, Linear operators, I. General theory, Interscience, N. Y. 1958.

    MATH  Google Scholar 

  10. C.M. Elson, An extension of Weyl's lemma to infinite dimensions, Trans. Amer. Math. Soc. 194 (1974), 301–324.

    MathSciNet  MATH  Google Scholar 

  11. S. V. Fomin, Differentiable measures in linear spaces, Uspehi Mat. Nauk 23 (1968), no. 1, 221–222.

    MathSciNet  MATH  Google Scholar 

  12. S. V. Fomin, Generalized functions of infinitely many variables and their Fourier transform, Uspehi Mat. Nauk 23 (1968) no. 2, 215–216.

    Google Scholar 

  13. S. V. Fomin, A Fourier transform method for functional differential equations, Soviet Math. Dokl. 9 (1968), 951–953.

    MATH  Google Scholar 

  14. L. Gross, Abstract Wiener spaces, Proc. Fifth Berkeley Sympos. Math. Statist. and Probability, vol. II, part 1 (1965), 31–42.

    Google Scholar 

  15. H.-H. Kuo, Integration by parts for abstract Wiener measures, Duke Math J. 41 (1974), 373–379.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. H.-H. Kuo, Differentiable measures, Chinese J. Math. 2 (1974), 188–198.

    MathSciNet  Google Scholar 

  17. H.-H. Kuo, Gaussian measures in Banach spaces, Lecture Notes in Math. Vol. 463, Springer-Verlag (1975).

    Google Scholar 

  18. H.-H. Kuo, Distribution theory on Banach space, Proc. First International Conference on Probability in Banach Spaces, Oberwolfach (1975), Lecture Notes in Math. Vol. 526 (1976), 143–156, Springer-Verlag.

    Google Scholar 

  19. H.-H. Kuo, On Gross differentiation on Banach spaces, Pacific J. Math. 59 (1975), 135–145.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. H.-H. Kuo, Uhlenbeck-Ornstein process on a Riemann-Wiener manifold, Proc. International Sympos. on Stochastic Differential Equations, Kyoto (1976), (to appear).

    Google Scholar 

  21. H.-H. Kuo, The chain rule for differentiable measures, Studia Math. (to appear).

    Google Scholar 

  22. H.-H. Kuo, Integration in Banach space, Lecture notes delivered in Math. Dept. Univ. Texas at Austin (1977).

    Google Scholar 

  23. M. Ann Piech, The Ornstein-Uhlenbeck semigroup in an infinite dimensional L2 setting, J. Functional Analysis 18 (1975), 271–285.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. I. E. Segal, Tensor algebras over Hilbert spaces, Trans, Amer. Math. Soc. 81 (1956), 106–134.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. A. V. Skorohod, Integration in Hilbert space, English transl., Springer-Verlag, 1974.

    Google Scholar 

  26. A. V. Uglanov, The heat equation for measures in a rigged Hilbert space, Moscow Univ. Math. Bulletin, 26 (1971), no.1–2, 42–48.

    MathSciNet  Google Scholar 

  27. A. V. Uglanov, Differentiable measures in a rigged Hilbert space, Moscow Univ. Math. Bulletin, 27 (1972), no. 5–6, 10–18.

    MathSciNet  MATH  Google Scholar 

  28. A. V. Uglanov, Differential equations with constant coefficients for generalized measures on Hilbert space, Math. USSR Izv. 9 (1975), no.2, 414–440.

    CrossRef  MathSciNet  MATH  Google Scholar 

  29. A. V. Uglanov, Second-order differential equations for functions of an infinite-dimensional argument, Soviet Math. Dokl. 17 (1976), no. 5, 1264–1267.

    MathSciNet  MATH  Google Scholar 

  30. P. Krée, Théories des Distributions et Calculs Différentiels sur un Espace de Banach, Seminaire P. Lelong (Analyse), 15e année, 1974/75.

    Google Scholar 

  31. B. Lascar, Propriétés d'espaces de Sobolev en dimension infinie, C. R. Acad. Sc. Paris, t. 280 (1975), Série A, 1587–1590.

    Google Scholar 

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© 1978 Springer-Verlag

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Kuo, HH. (1978). Differential calculus for measures on Banach spaces. In: Aron, R.M., Dineen, S. (eds) Vector Space Measures and Applications I. Lecture Notes in Mathematics, vol 644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066851

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  • DOI: https://doi.org/10.1007/BFb0066851

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