Keywords
- Local Measure
- Borel Measure
- Differential Calculus
- Logarithmic Derivative
- Decomposition Property
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References
J.I. Alvarez, The Riesz decomposition theorem for distributions on a Wiener space, Ph. D. Thesis, Cornell University, Ithaca, N. Y. (1973)
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.
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.
Yu. M. Berezanskii and Yu. S. Samoilenko, Nuclear spaces of functions of infinitely many variables, Ukrainian Math. J. 25 (1973), 599–609.
Ju. L. Daleckiľ, Infinite-dimensional elliptic operators and the corresponding parabolic equations, Russian Math. Surveys 22 (1967), no. 4, 1–53.
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.
D. N. Dudin, Theory of distributions on Hilbert space, Uspehi Mat. Nauk 27 (1972), no.2, 169–170.
D. N. Dudin, Generalized measures or distributions on Hilbert space, Trans. Moscow Math. Soc. 28 (1973), 133–157.
N. Dunford and J. T. Schwartz, Linear operators, I. General theory, Interscience, N. Y. 1958.
C.M. Elson, An extension of Weyl's lemma to infinite dimensions, Trans. Amer. Math. Soc. 194 (1974), 301–324.
S. V. Fomin, Differentiable measures in linear spaces, Uspehi Mat. Nauk 23 (1968), no. 1, 221–222.
S. V. Fomin, Generalized functions of infinitely many variables and their Fourier transform, Uspehi Mat. Nauk 23 (1968) no. 2, 215–216.
S. V. Fomin, A Fourier transform method for functional differential equations, Soviet Math. Dokl. 9 (1968), 951–953.
L. Gross, Abstract Wiener spaces, Proc. Fifth Berkeley Sympos. Math. Statist. and Probability, vol. II, part 1 (1965), 31–42.
H.-H. Kuo, Integration by parts for abstract Wiener measures, Duke Math J. 41 (1974), 373–379.
H.-H. Kuo, Differentiable measures, Chinese J. Math. 2 (1974), 188–198.
H.-H. Kuo, Gaussian measures in Banach spaces, Lecture Notes in Math. Vol. 463, Springer-Verlag (1975).
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.
H.-H. Kuo, On Gross differentiation on Banach spaces, Pacific J. Math. 59 (1975), 135–145.
H.-H. Kuo, Uhlenbeck-Ornstein process on a Riemann-Wiener manifold, Proc. International Sympos. on Stochastic Differential Equations, Kyoto (1976), (to appear).
H.-H. Kuo, The chain rule for differentiable measures, Studia Math. (to appear).
H.-H. Kuo, Integration in Banach space, Lecture notes delivered in Math. Dept. Univ. Texas at Austin (1977).
M. Ann Piech, The Ornstein-Uhlenbeck semigroup in an infinite dimensional L2 setting, J. Functional Analysis 18 (1975), 271–285.
I. E. Segal, Tensor algebras over Hilbert spaces, Trans, Amer. Math. Soc. 81 (1956), 106–134.
A. V. Skorohod, Integration in Hilbert space, English transl., Springer-Verlag, 1974.
A. V. Uglanov, The heat equation for measures in a rigged Hilbert space, Moscow Univ. Math. Bulletin, 26 (1971), no.1–2, 42–48.
A. V. Uglanov, Differentiable measures in a rigged Hilbert space, Moscow Univ. Math. Bulletin, 27 (1972), no. 5–6, 10–18.
A. V. Uglanov, Differential equations with constant coefficients for generalized measures on Hilbert space, Math. USSR Izv. 9 (1975), no.2, 414–440.
A. V. Uglanov, Second-order differential equations for functions of an infinite-dimensional argument, Soviet Math. Dokl. 17 (1976), no. 5, 1264–1267.
P. Krée, Théories des Distributions et Calculs Différentiels sur un Espace de Banach, Seminaire P. Lelong (Analyse), 15e année, 1974/75.
B. Lascar, Propriétés d'espaces de Sobolev en dimension infinie, C. R. Acad. Sc. Paris, t. 280 (1975), Série A, 1587–1590.
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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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