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Compactifications of harmonic spaces and Hunt processes

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1351)

Keywords

  • Riemann Surface
  • Boundary Behavior
  • Harmonic Morphism
  • Harmonic Space
  • Superharmonic Function

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References

  1. J. Bliedtner-W. Hansen, Potential theory — An analytic and probabilistic approach to balayage, Universitext, Springer-Verlag, 1986.

    Google Scholar 

  2. C. Constantinescu-A. Cornea, Potential theory on harmonic spaces, Grundl. der math. Wiss., 158, Springer-Verlag, 1972.

    Google Scholar 

  3. C. Dellacherie-P. A. Meyer, Probabilities and potential B, North-Holland Math. Studies, 72, North-Holland, 1982.

    Google Scholar 

  4. J. L. Doob, Conditional Brownian motion and the boundary limits of harmonic functions, Bull. Soc. Math. France 85 (1957), 431–458.

    MathSciNet  MATH  Google Scholar 

  5. J. L. Doob, Conformally invariant cluster value theory, Illinois J. Math. 5 (1961), 521–549.

    MathSciNet  MATH  Google Scholar 

  6. J. L. Doob, Classical potential theory and its probabilistic counterpart, Grundl. der math. Wiss., 262, Springer-Verlag, 1984.

    Google Scholar 

  7. J. Hyvönen, On resolutive compactifications of harmonic spaces, Ann. Acad. Sci. Fenn. Ser A I Math. Dissertations 8 (1976).

    Google Scholar 

  8. T. Ikegami, The boundary behavior of analytic mappings of Riemann surfaces, Complex Analysis (Joensuu, 1978), 161–166, Lecture Notes in Math., 747, Springer-Verlag, 1979.

    Google Scholar 

  9. T. Ikegami, Compactifications of Martin type of harmonic spaces, Osaka J. Math. 23 (1986), 653–680.

    MathSciNet  MATH  Google Scholar 

  10. T. Ikegami, On the boundary behavior of harmonic morphisms at the boundary of compactifications of Martin type, to appear in Osaka J. Math.

    Google Scholar 

  11. C. Meghea, Compactification des espaces harmoniques, Lecture Notes in Math., 222, Springer-Verlag, 1971.

    Google Scholar 

  12. L. Naïm, Sur le rôle de la frontière de R. S. Martin dans la théorie du potentiel, Ann. Inst. Fourier 7 (1957), 183–281.

    CrossRef  MATH  Google Scholar 

  13. K. Oja, On cluster sets of harmonic morphisms between harmonic spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 24 (1979).

    Google Scholar 

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© 1988 Springer-Verlag

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Ikegami, T. (1988). Compactifications of harmonic spaces and Hunt processes. In: Laine, I., Sorvali, T., Rickman, S. (eds) Complex Analysis Joensuu 1987. Lecture Notes in Mathematics, vol 1351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081254

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  • DOI: https://doi.org/10.1007/BFb0081254

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50370-5

  • Online ISBN: 978-3-540-45992-7

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