Extremizations and Dirichlet integrals on Riemann surfaces

Mitsuru NAKAI

doi:10.2969/jmsj/02830581

Mitsuru NAKAI

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JOURNAL FREE ACCESS

1976 Volume 28 Issue 3 Pages 581-603

DOI https://doi.org/10.2969/jmsj/02830581

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Published: 1976 Received: September 09, 1975 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Leo Sario on his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) M. Glasner and R. Katz, On the behavior of solutions of Δu=Pu at the Royden boundary, J, d'Analyse Math., 22 (1969), 345-354.
2) M. Nakai, Dirichlet finite solutions of Δu=Pu on open Riemann surfaces, Kodai Math. Sem. Rep., 23 (1971), 385-397.
3) M. Nakai, Order comparisons on canonical isomorphisms, Nagoya Math. J., 50 (1973), 67-87.
4) M. Nakai, Canonical isomorphisms of energy finite solutions of Δu=Pu on open Riemann surfaces, Nagoya Math. J., 56 (1974), 79-84.
5) M. Nakai, An example on canonical isomorphism, Seminar Note, 1975.
6) H. Royden, The equation Δu=Pu, and the classification of open Riemann surfaces, Ann. Acad. Sci. Fenn. 271 (1959), 1-27.
7) L. Sario and M. Nakai, Classification Theory of Riemann Surfaces, Springer, 1970.
8) I. Singer, Dirichlet finite solutions of Δu=Pu, Proc. Amer. Math. Soc., 32 (1972), 464-468.
9) I. Singer, Boundary isomorphism between Dirichlet finite solutions of Δu=Pu and harmonic functions, Nagoya Math. J., 50 (1973), 7-20.
10) M. Tsuji, Potential Theory in Modern Function Theory, Maruzen, 1959.
11) K. Yosida, Functional Analysis, Springer, 1965.

Right : [1] M. Glasner and R. Katz, On the behavior of solutions of Δu=Pu at the Royden boundary, J. d'Analyse Math., 22 (1969), 345-354.
[2] M. Nakai, Dirichlet finite solutions of Δu=Pu on open Riemann surfaces, Kodai Math. Sem. Rep., 23 (1971), 385-397.
[3] M. Nakai, Order comparisons on canonical isomorphisms, Nagoya Math. J., 50 (1973), 67-87.
[4] M. Nakai, Canonical isomorphisms of energy finite solutions of Δu=Pu on open Riemann surfaces, Nagoya Math. J., 56 (1974), 79-84.
[5] M. Nakai, An example on canonical isomorphism, Seminar Note, 1975.
[6] H. Royden, The equation Δu=Pu, and the classification of open Riemann surfaces, Ann. Acad. Sci. Fenn. 271 (1959), 1-27.
[7] L. Sario and M. Nakai, Classification Theory of Riemann Surfaces, Springer, 1970.
[8] I. Singer, Dirichlet finite solutions of Δu=Pu, Proc. Amer. Math. Soc., 32 (1972), 464-468.
[9] I. Singer, Boundary isomorphism between Dirichlet finite solutions of Δu=Pu and harmonic functions, Nagoya Math. J., 50 (1973), 7-20.
[10] M. Tsuji, Potential Theory in Modern Function Theory, Maruzen, 1959.
[11] K. Yosida, Functional Analysis, Springer, 1965.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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