Brelot spaces of Schrödinger equations

Mitsuru NAKAI

doi:10.2969/jmsj/04820275

Mitsuru NAKAI

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JOURNAL FREE ACCESS

1996 Volume 48 Issue 2 Pages 275-298

DOI https://doi.org/10.2969/jmsj/04820275

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Published: 1996 Received: September 01, 1993 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: CITATION Details: Wrong : 1) M. Aizenman and B. Simon, Brownian motion and Harnack inequality for Schrödinger operators, Comm. Pure Appl. Math., 35 (1982), 209-273.
2) S. Axler, P. Bourdon and W. Ramey, Harmonic Function Theory, Springer, 1992.
3) A. Boukricha, Das Picard-Prinzip and verwandte Fragen bei Störung von harmonischen Räumen, Math. Ann., 239 (1979), 247-270.
4) A. Boukricha, W. Hansen and H. Hueber, Continuous solutions of the generalized Schrödinger equation and perturbation of harmonic spaces, Exposition. Math., 5 (1987), 97-135.
5) C. Constantinescu and A. Cornea, Potential Theory on Harmonic Spaces, Springer, 1969.
6) L. L. Helms, Introduction to Potential Theory, Wiley-Interscience, 1969.
7) Ü. Kuran, A new criterion of Dirichlet regularity via quasi-boundedness of the fundamental superharmonic function, J. London Math. Soc., 19 (1979), 301-311.
8) P. A. Loeb and B. Walsh, The equivalence of Harnack's principle and Harnack's inequality in the axiomatic system of Brelot, Ann. Inst. Fourier, 15 (1965), 597-600.
9) F.-Y. Maeda, Dirichlet Integrals on Harmonic Spaces, Lecture Notes in Math., 803, Springer, 1980.
10) M. Nakai, Continuity of solutions of Schrödinger equations, Math. Proc. Cambridge Philos. Soc., 110 (1991), 581-597.
11) K. T. Sturm, Schrödinger semigroups on manifolds, J. Funct. Anal., 118 (1993), 309-350.
12) J. Wermer, Potential Theory, Lecture Notes in Math., 408, Springer, 1974.
13) Z. Zhao, Green function for Schrödinger operator and conditioned Feynman-Kac gauge, J. Math. Anal. Appl., 116 (1986), 309-334.

Right : [1] M. Aizenman and B. Simon, Brownian motion and Harnack inequality for Schrödinger operators, Comm. Pure Appl. Math., 35 (1982), 209-273.
[2] S. Axler, P. Bourdon and W. Ramey, Harmonic Function Theory, Springer, 1992.
[3] A. Boukricha, Das Picard-Prinzip und verwandte Fragen bei Störung von harmonischen Räumen, Math. Ann., 239 (1979), 247-270.
[4] A. Boukricha, W. Hansen and H. Hueber, Continuous solutions of the generalized Schrödinger equation and perturbation of harmonic spaces, Exposition. Math., 5 (1987), 97-135.
[5] C. Constantinescu and A. Cornea, Potential Theory on Harmonic Spaces, Springer, 1969.
[6] L. L. Helms, Introduction to Potential Theory, Wiley-Interscience, 1969.
[7] Ü. Kuran, A new criterion of Dirichlet regularity via quasi-boundedness of the fundamental superharmonic function, J. London Math. Soc., 19 (1979), 301-311.
[8] P. A. Loeb and B. Walsh, The equivalence of Harnack's principle and Harnack's inequality in the axiomatic system of Brelot, Ann. Inst. Fourier, 15 (1965), 597-600.
[9] F. -Y. Maeda, Dirichlet Integrals on Harmonic Spaces, Lecture Notes in Math., 803, Springer, 1980.
[10] M. Nakai, Continuity of solutions of Schrödinger equations, Math. Proc. Cambridge Philos. Soc., 110 (1991), 581-597.
[11] K. T. Sturm, Schrödinger semigroups on manifolds, J. Funct. Anal., 118 (1993), 309-350.
[12] J. Wermer, Potential Theory, Lecture Notes in Math., 408, Springer, 1974.
[13] Z. Zhao, Green function for Schrödinger operator and conditioned Feynman-Kac gauge, J. Math. Anal. Appl., 116 (1986), 309-334.

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

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