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Harmonic spaces with positive potentials and nonconstant harmonic functions

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On a Harmonic Space Satisfying the axioms 1, 2, 3 of M. Brelot and having positive potentials, the existence of nonconstant harmonic functions is studied, following the lines of the classification of a hyperbolic Riemann Surface.

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Bibliography

  1. I. V. Anandam,Espaces Harmoniques Sans Potentiel Positif, Ann. Inst. Fourier, t. 22 (1972), (to appear).

  2. M. Brelot,Lectures on Potential Theory, Tata Institute of Fundamental Research, Bombay, 1960 (re-issued 1967).

    MATH  Google Scholar 

  3. M. Brelot,Axiomatique des fonctions harmoniques, Cours d'été 1965, Montréal, Les Presses de l’Université 1966.

    Google Scholar 

  4. C. Constantinescu and A. Cornea,Ideale Ränder Riemannscher Flächen, Ergeb. 32, Springer 1963.

  5. C. Constantinescu and A. Cornea,Compactifications of harmonic spaces, Nagoya Math. Journal, t. 25 (1965), pp. 1–57.

    MATH  MathSciNet  Google Scholar 

  6. K. Gowrisankaran,Fatou-Naim-Doob limit theorems in the axiomatic system of Brelot, Ann. Inst. Fourier, t. 16/2 (1966), pp. 455–467.

    MathSciNet  Google Scholar 

  7. M. Heins,On the principle of harmonic measure, comment, Math. Helv., t. 33 (1959), pp. 47–58.

    Article  MATH  MathSciNet  Google Scholar 

  8. Mme. R.-M. Hervé,Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel, Ann. Inst. Fourier, t. 12 (1962), pp. 415–571.

    MATH  Google Scholar 

  9. M. Nakai, Φbounded harmonic functions, Ann. Inst. Fourier, t. 16/1 (1966) pp. 145–157.

    MathSciNet  Google Scholar 

  10. L. Sario and M. Nakai,Classification Theory of Riemann Surfaces, Springer-Verlag, 1970.

  11. B. Walsh,Flux in axiomatic potential Theory I, Inventiones Math., t. 8/3 (1969).

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Anandam, I.V. Harmonic spaces with positive potentials and nonconstant harmonic functions. Rend. Circ. Mat. Palermo 21, 149–167 (1972). https://doi.org/10.1007/BF02844239

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