Hiroshima Mathematical Journal

Dirichlet integrals of functions on a self-adjoint harmonic space

Fumi Yuki Maeda

Full-text: Open access

Article information

Source
Hiroshima Math. J., Volume 4, Number 3 (1974), 685-742.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206136844

Digital Object Identifier
doi:10.32917/hmj/1206136844

Mathematical Reviews number (MathSciNet)
MR0364660

Zentralblatt MATH identifier
0298.31013

Subjects
Primary: 31D05: Axiomatic potential theory

Citation

Maeda, Fumi Yuki. Dirichlet integrals of functions on a self-adjoint harmonic space. Hiroshima Math. J. 4 (1974), no. 3, 685--742. doi:10.32917/hmj/1206136844. https://projecteuclid.org/euclid.hmj/1206136844


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References

  • [1] H. Bauer, Harmonische Rume und ihre Potentialtheorie, Lecture Notes in Math. 22, Springer-Verlag, Berlin-Heidelberg-New York,1966.
  • [2] N. Boboc, C. Constantinescu and A. Cornea, On the Dichlet problem in the axiomatic theory of harmonic functions, Nagoya Math. J. 23 (1963), 73-96.
  • [3] M. Brelot, Lectures on potential theory, Tata Inst. of F. R., Bombay, 1960 (reissued 1967).
  • [4] C. Constantinescu and A. Cornea, Ideale Rnder Riemannscher Flchen, Springer-Verlag, Berlin-Gttingen-Heidelberg, 1963.
  • [5] C. Constantinescu and A. Cornea, Potential theory on harmonic spaces, Springer-Verlag, Berlin-Heidelberg-New York,1972.
  • [6] M. Glasner and M. Nakai, Riemannian manifolds with discontinuous metrics and the Dirichlet integral, Nagoya Math. J. 46 (1972), 1-48.
  • [7] R.-M. Herve, Recherches axiomatiques sur la theorie des functions sur harmoniques et du potentiel, Ann. Inst. Fourier 12 (1962), 415-571.
  • [8] F-Y. Maeda, Harmonic and full-harmonic structures on a differentiable manifold, J. Sci. HiroshimaUniv., Ser.A-I 34 (1970), 271-312.
  • [9] F-Y. Maeda, Energy of functions on a self-adjoint harmonic space I and //, Hiroshima Math. J. 2 (1972), 313-337 and 3 (1973), 37-60.
  • [10] F-Y. Maeda, On the Green function of a self-adjoint harmonic space, Ibid. 3 (1973), 361-366.
  • [11] M. Nakai, The space of Dirichlet-like solutions of the equation u=Pu on a Riemann surface, Nagoya Math. J. 18 (1961), 111-131.
  • [12] B. Walsh, Perturbation of harmonic structures and an index-zero theorem, Ann. Inst. Fourier 20, 1 (1970), 317-359.