Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-06T07:15:56.840Z Has data issue: false hasContentIssue false
  • English
  • Français

An example on canonical isomorphism

Published online by Cambridge University Press:  22 January 2016

Mitsuru Nakai
Mitsuru Nakai*
Affiliation:
Department of Mathematics, Nagoya Institute of Technology, Gokiso, Showa, Nagoya 466, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A nonnegative locally Hölder continuous second order differential P = P(z)dxdy (z = x + iy) on a Riemann surface R is referred to as a density on R. A density P is said to be finite if P is integrable over R, i.e.

(1) ∫ R P(z)dxdy < ∞.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 70 , July 1978 , pp. 25 - 40
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1978

References

[1] Nakai, M.: Dirichlet finite solutions of an—Fu on open Riemann surfaces, Kōdai Math. Sem. Rep., 23 (1971), 385–397.Google Scholar
[2] Nakai, M.: Order comparisons on canonical isomorphism, Nagoya Math. J., 50 (1973), 67–87.Google Scholar
[3] Nakai, M.: Canonical isomorphisms of energy finite solutions of au—Pu on open Riemann surfaces, Nagoya Math. J., 56 (1975), 79–84.Google Scholar
[4] Sario, L. and Nakai, M.: Classification Theory of Riemann Surfaces, Springer, 1970.Google Scholar
[5] Singer, I.: Dirichlet finite solutions of Aw—Pu , Proc. Amer. Math. Soc, 32 (1972), 464–468.Google Scholar
[6] Singer, I.: Boundary isomorphism between Dirichlet finite solutions of au—Pu and harmonic functions, Nagoya Math. J., 50 (1973), 7–20.Google Scholar
[7] Tsuji, M.: Potential Theory in Modern Function Theory, Maruzen, 1959.Google Scholar
[8] Yosida, K.: Functional Analysis, xsSpringer 1965.Google Scholar