Skip to main content

Infinite dimensional newtonian potentials

Part of the Lecture Notes in Mathematics book series (LNM,volume 828)

Abstract

We give a survey of various curiosities and problems concerning potential theory of infinite dimensional Brownian motion processes.

Keywords

  • Invariant Function
  • Gaussian Measure
  • Transition Kernel
  • Complete Orthonormal System
  • Finite Dimensional Case

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Talk given at the Second International Conference "Probability Theory on Vector Spaces" held in Blazejewko (Poland) in September 1979

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. BORELL: Random linear functionals and subspaces of probability one. Ark. Mat. 14 (1976) 79–92.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. R. CARMONA: Potentials on Abstract Wiener Space. J. Functional Anal. 26 (1977) 215–231.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. R. CARMONA: Tensor product of Gaussian measures. in "Vector Space Measures and Applications I" Proc. Dublin 1977 ed. R.M.Aron and S.Dineen Lect. Notes in Math. #644 p.96–124.

    Google Scholar 

  4. J. DENY: Noyaux de convolution de Hunt et noyaux associés à une famille fondamentale. Ann. Inst. Fourier 12 (1962) 643–667.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. X. FERNIQUE: Intégrabilité des vecteurs gaussiens. C.R.Acad.Sci. Paris, ser.A 270 (1970) 1698–1699.

    MathSciNet  MATH  Google Scholar 

  6. V. GOODMAN: A Liouville theorem for abstract Wiener spaces. Amer. J. Math. 95 (1973) 215–220.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. L. GROSS: Abstract Wiener Spaces. Proc. Fifth Berkeley Symp. on Math. Stat. and Prob. vol.II Univ. California Press (1967) p.31–42.

    Google Scholar 

  8. L. GROSS: Potential Theory on Hilbert Space. J. Functional Anal. 1 (1967) 123–181.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. G.A. HUNT: Markoff Processes and Potentials I. Ill. J. Math. 1 (1957) 44–93.

    MathSciNet  MATH  Google Scholar 

  10. H.H.KUO: Gaussian Measures in Banach Spaces. Lect. Notes in Math. #463 (1975).

    Google Scholar 

  11. P.A.MEYER: Processus de Markov. Lect. Notes in Math. #26 (1967).

    Google Scholar 

  12. M.A. PIECH: Regularity of the Green operator on abstract Wiener space. J. Differential Equat. 12 (1972) 353–360.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. S.C.PORT and C.J.STONE: Brownian Motion and Classical Potential Theory. Academic Press (1978).

    Google Scholar 

  14. H. ROST: Die Stoppverteilungen eines Markoff-Prozesses mit lokalendlichem Poten tial. Manuscripta Math. 3 (1970) 321–330.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Carmona, R. (1980). Infinite dimensional newtonian potentials. In: Weron, A. (eds) Probability Theory on Vector Spaces II. Lecture Notes in Mathematics, vol 828. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097392

Download citation

  • DOI: https://doi.org/10.1007/BFb0097392

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10253-3

  • Online ISBN: 978-3-540-38350-5

  • eBook Packages: Springer Book Archive