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Potential theory on Hilbert space. (English) Zbl 0165.16403

Full Text: DOI
[1] Bonic, R.; Frampton, J.: Differentiable functions on certain Banach spaces. Bull. am. Math. soc. 71, 393-395 (1965) · Zbl 0131.12905
[2] Daletzky, Yu.L: Differential equations with functional derivatives and stochastic equations for generalized random processes. Dokl. akad. Nauk SSSR 166, 1035-1038 (1966)
[3] Dini, V.: Sur la méthode des approximations successives pour LES équations aux dérivées partielles du deuxième ordre. Acta. math. 25, 185-230 (1902) · Zbl 32.0366.03
[4] Doob, J. L.: Semimartingales and subharmonic functions. Trans. am. Math. soc. 77, 86-121 (1954) · Zbl 0059.12205
[5] Dynkin, E. B.: Markov processes--I. (1965) · Zbl 0132.37901
[6] Feldman, J.: Equivalence and perpendicularity of Gaussian processes. Pacific J. Math. 8, 699-708 (1958) · Zbl 0084.13001
[7] Gelfand, I. M.; Vilenkin, N. Ya: Some applications of harmonic analysis-augmented Hilbert spaces. Generalized functions 4 (1961)
[8] Gross, L.: Integration and nonlinear transformations in Hilbert space. Trans. am. Math. soc. 94, 404-440 (1960) · Zbl 0090.33303
[9] Gross, L.: Measurable functions on Hilbert space. Trans. am. Math. soc. 105, 372-390 (1962) · Zbl 0178.50001
[10] Gross, L.: Classical analysis on a Hilbert space. Analysis in function space (1964) · Zbl 0126.16401
[11] Gross, L., Abstract Wiener spaces, in ”Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability” (to be published). · Zbl 0187.40903
[12] Hunt, G. A.: Some theorems concerning Brownian motion. Trans. am. Math. soc. 81, 294-319 (1956) · Zbl 0070.36601
[13] Kurzweil, J.: On approximation in real Banach spaces. Studia math. 14, 213-231 (1954)
[14] Levy, P.: Leçons d’analyse fonctionelle. (1922)
[15] Levy, P.: Analyse fonctionelle. Mem. sci. Math. acad. Sci. Paris (1925)
[16] Levy, P.: Problèmes concrets d’analyse fonctionelle. (1951)
[17] Levy, P.: Random functionsl a Laplacian random function depending on a point of Hilbert space. Univ. calif. Publ. statistics 2, No. No. 10, 195-206 (1956)
[18] Nelson, E.: An existence theorem for second order parabolic equations. Trans. am. Math. soc. 88, 414-429 (1958) · Zbl 0115.31101
[19] Petrini, H.: LES dérivées premières et secondes du potentiel. Acta. math. 31, 127-332 (1908) · Zbl 39.0819.01
[20] Prochorov, Yu.V: The method of characteristic functionals. Proceedings of the fourth Berkeley symposium on mathematical statistics and probability, 403-419 (1961)
[21] Schatten, R.: A theory of cross spaces. (1950) · Zbl 0041.43502
[22] Segal, I. E.: Distributions in Hilbert space and canonical systems of operators. Trans. am. Math. soc. 88, 12-41 (1958) · Zbl 0099.12104
[23] Varadhan, S. R. S: Limit theorems for sums of independent random variables with values in a Hilbert space. Sankhya, ser. A 24, 213-238 (1962) · Zbl 0113.34101
[24] Whitfield, J. H. M: Differentiable functions with bounded nonempty support on Banach spaces. Bull. am. Math. soc. 72, 145-146 (1966) · Zbl 0134.32404