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manuscripta mathematica

, Volume 1, Issue 3, pp 289–292 | Cite as

On the analytic structure of harmonic groups

  • Jürgen Bliedtner
Article

Abstract

It will be shown that for any left-harmonic group (G,þ) the locally compact group G is a Lie group. If moreover G is abelian and connected then G =Rn.

Keywords

Analytic Structure Number Theory Algebraic Geometry Topological Group Compact Group 
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.

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References

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    BAUER, H.: Harmonische Räume und ihre Potential theorie. Lecture Notes in Mathematics, 22. Berlin-Heidelberg-New York: Springer 1966.Google Scholar
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    BLIEDTNER, J.: Harmonische Gruppen und Huntsche Faltungskerne. Seminar über Potentialtheorie. Lecture Notes in Mathematics, 69. Berlin-Heidelberg-New York: Springer 1968.Google Scholar
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    BOBOC, N., CONSTANTINESCU, C. and CORNEA, A.: Axiomatic theory of harmonic functions. Non-negative superharmonic functions. Ann. Inst. Fourier 15/1, 283–312 (1965).Google Scholar
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    BOBOC, N., CONSTANTINESCU, C. and CORNEA, A.: Axiomatic theory of harmonic functions. Balayage. Ann. Inst. Fourier 15/2, 37–70 (1965).Google Scholar
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    BONY, J.-M.: Détermination des axiomatiques de théorie du potentiel dont les fonctions harmoniques sont différentiables. Ann. Inst. Fourier 17/1, 353–382 (1967).Google Scholar
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    CONSTANTINESCU, C: Some properties of the balayage of measures on a harmonic space. Ann. Inst. Fourier 17/1, 273–293 (1967).Google Scholar
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    HEYER, H.: Factorization of probability measures on locally compact groups. Z. Wahrscheinlichkeitstheorie verw. Geb. 8, 231–258 (1967).Google Scholar
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    MONTGOMERY, D. and ZIPPIN, L.: Topological transformation groups. 3rd print. New York: Interscience Publishers, Inc. 1965.Google Scholar

Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • Jürgen Bliedtner
    • 1
  1. 1.Mathematisches InstitutUniversität Erlangen-NürnbergErlangen

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