Published: 1985 Received: May 16, 1983Available on J-STAGE: October 20, 2006Accepted: -
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Date of correction: October 20, 2006Reason for correction: -Correction: CITATIONDetails: Wrong : 1) J. Abraham and J. E. Marsden, Foundations of mechanics, 2nd ed., Benjamin, Massachusetts, 1978. 2) T. Aubin, Nonlinear analysis on manifolds. Monge-Ampere equations, A series of comprehensive studies in mathematics, 252, Springer, 1982. 3) M. Berger, P, Gauduchon and E. Mazet, Le spectre d'une variete Riemannienne, Lecture Notes in Math., 140, Springer, 1966. 4) J. Cheeger and D. G. Ebin, Comparison theorems in Riemannian geometry, North-Holland, Amsterdam, 1975. 5) A. J. Chorin, T. J. R. Hughes, M. F. McCraken and J. E. Marsden, Product formulas and numerical algorithms, Comm. Pure Appl. Math., 31 (1978), 205-256. 6) B. S. de Witt, Dynamical theory in curved spaces, I, A review of the classical and quantum action principles, Rev. Modern Phys., 29 (1957), 377-397. 7) R. P. Feynman, Space time approach to non-relativistic quantum mechanics, Rev. Modern Phys., 20 (1948), 367-387. 8) D. Fujiwara, A construction of the fundamental solution for the Schrödinger equation, J. Analyse Math., 35 (1979), 41-56. 9) D. Fujiwara, Remarks on convergence of the Feynman path integrals, Duke Math. J., 47 (1980), 559-600. 10) E. Hille and R. S. Phillips, Functional analysis and semi-groups, Amer. Math. Soc., Providence, 1957. 11) A. Inoue and Y. Maeda, On integral transformations associated with a certain Riemannian metric, Proc. Japan Acad. Ser. A, 58 (1982), 281-284. 12) Y. Maeda, Pointwise convergence of the product integral for a certain integral transformation associated with a Riemannian metric, to appear in Kodai Math. J. 13) J. Milnor, Morse theory, Annals of Math. Studies, Princeton Univ. Press, 1963. 14) T. Sakai, On eigenvalues of Laplacian and curvature of Riemannian manifold, Tohoku Math. J., 23 (1971), 589-603.
Right : [1] J. Abraham and J. E. Marsden, Foundations of mechanics, 2nd ed., Benjamin, Massachusetts, 1978. [2] T. Aubin, Nonlinear analysis on manifolds. Monge-Ampere equations, A series of comprehensive studies in mathematics, 252, Springer, 1982. [3] M. Berger, P, Gauduchon and E. Mazet, Le spectre d'une variete Riemannienne, Lecture Notes in Math., 140, Springer, 1966. [4] J. Cheeger and D. G. Ebin, Comparison theorems in Riemannian geometry, North-Holland, Amsterdam, 1975. [5] A. J. Chorin, T. J. R. Hughes, M. F. McCraken and J. E. Marsden, Product formulas and numerical algorithms, Comm. Pure Appl. Math., 31 (1978), 205-256. [6] B. S. de Witt, Dynamical theory in curved spaces, I, A review of the classical and quantum action principles, Rev. Modern Phys., 29 (1957), 377-397. [7] R. P. Feynman, Space time approach to non-relativistic quantum mechanics, Rev. Modern Phys., 20 (1948), 367-387. [8] D. Fujiwara, A construction of the fundamental solution for the Schrödinger equation, J. Analyse Math., 35 (1979), 41-56. [9] D. Fujiwara, Remarks on convergence of the Feynman path integrals, Duke Math. J., 47 (1980), 559-600. [10] E. Hille and R. S. Phillips, Functional analysis and semi-groups, Amer. Math. Soc., Providence, 1957. [11] A. Inoue and Y. Maeda, On integral transformations associated with a certain Riemannian metric, Proc. Japan Acad. Ser. A, 58 (1982), 281-284. [12] Y. Maeda, Pointwise convergence of the product integral for a certain integral transformation associated with a Riemannian metric, to appear in Kodai Math. J. [13] J. Milnor, Morse theory, Annals of Math. Studies, Princeton Univ. Press, 1963. [14] T. Sakai, On eigenvalues of Laplacian and curvature of Riemannian manifold, Tôhoku Math. J., 23 (1971), 589-603.
Date of correction: October 20, 2006Reason for correction: -Correction: PDF FILEDetails: -