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Hyperharmonic Cones

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Potential Theory

Abstract

The theory of H-cones ([3]) covers the superharmonic case in potential theory. This work continues the algebraic axiomatization of the hyperharmonic case. Our basic structure is a hyperharmonic structure defined by M. Arsove and H. Leutwiler in [1]. The cancellation law does not hold in hyperharmonic structures. In order to characterize cancellable elements we assume that a hyperharmonic structure is a convex cone and the greatest lower bound of (u/n) nεℕ exists for all u.

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References

  1. Arsove M.G. and H. Leutwiler: Algebraic potential theory. Mem. Amer. Math. Soc. 226 (1980).

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  2. Arsove M.G. and H. Leutwiler: Quasi-units in mixed lattices structures. Lecture Notes in Math. 789, Springer-Verlag, Berlin-Heidelberg-New York (1979), 35–54.

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  3. Boboc N., Gh. Bucur and A. Cornea: Order and convexity in potential theory: H-cones. Lecture Notes in Math. 853, Springer-Verlag, Berlin-Heidelberg-New York (1981).

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  4. Boboc, N. and A. Cornea: H-cônes et biadjoints des H-cônes. C. R. Acad. Sci. Paris 270 (1970) 1679–1682.

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  5. Cornea, A. and S.-L. Eriksson: Order continuity of the greatest lower bound of two functionals. Analysis 7 (1987) 173–184.

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  6. Cornea, A. and G. Licea: Order and potential resolvent families of kernels. Lecture Notes in Math. 494, Springer-Verlag, Berlin-Heidelberg-New York (1975).

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  7. Eriksson, S.-L.: Hyperharmonic cones and hyperharmonic morphims. Ann. Acad. Sci. Fenn. Ser. AI Math. Dissertationes 49 (1984).

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  8. Eriksson, S.-L.: Hyperharmonic cones and cones of hyperharmonics. An. Stiint. Univ. “AI.I.Cuza” Iasi Sect Ia Mat. (1985), 109–116.

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  9. Eriksson, S.-L.: Representations of hyperharmonic cones. To appear in Trans. Amer. Math. Soc.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Joensuu, SF-80101, Joensuu, Finland

    Sirkka-Liisa Eriksson-Bique

Authors
  1. Sirkka-Liisa Eriksson-Bique
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Editor information

Editors and Affiliations

  1. Czechoslovak Academy of Sciences, Prague, Czechoslovakia

    Josef Král

  2. Charles University, Prague, Czechoslovakia

    Jaroslav Lukeš , Ivan Netuka  & Jiří Veselý ,  & 

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© 1988 Plenum Press, New York

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Eriksson-Bique, SL. (1988). Hyperharmonic Cones. In: Král, J., Lukeš, J., Netuka, I., Veselý, J. (eds) Potential Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0981-9_12

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  • DOI: https://doi.org/10.1007/978-1-4613-0981-9_12

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-8276-1

  • Online ISBN: 978-1-4613-0981-9

  • eBook Packages: Springer Book Archive

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