On the Poisson Equation on the Infinite Dimensional Torus

  • Alexander D. Bendikov
  • Igor V. Pavlov


Let {μt}t>0 be the Wiener semigroup on the infinite dimensional torus T (cf. Heyer,5 Ch. 5). Let us consider the Green measure
$$G(dy) = \int\limits_0^\infty {e^{ - t} \mu _t (dy)dt}$$




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  1. 1.
    A.D.Bendikov, I.V.Pavlov, Diffusion processes on the group T¥ and elliptic equations with infinite numbers of variables, in: “Probability Theory and Mathematical Statistics,” V.1: 145–169, Yu.V. Prohorov et al. ed., VNU Science Press BV, Utrecht (1987).Google Scholar
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    Ch.Berg, Potential theory on the infinite dimensional torus, Invent. Math. 32: 49–100 (1976).MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    H.Heyer, “Probability Measures on Locally Compact Groups,” Springer-Verlag, Berlin — Heidelberg (1977).MATHGoogle Scholar
  4. 4.
    E.M.Stein,“Singular Integrals and Differentiability Properties of Functions,” Princeton Univ. Press, Guildford (1970).MATHGoogle Scholar
  5. 5.
    K.Yosida, “Functional Analysis,” Springer-Verlag, Berlin — Heidel berg (1980).MATHGoogle Scholar

Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • Alexander D. Bendikov
    • 1
  • Igor V. Pavlov
    • 1
  1. 1.Rostov Civil Engineering InstituteRostov-on-DonUSSR

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