A construction of fundamental solution of Schrödinger's equation on the sphere

Daisuke FUJIWARA

doi:10.2969/jmsj/02830483

Daisuke FUJIWARA

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JOURNAL FREE ACCESS

1976 Volume 28 Issue 3 Pages 483-505

DOI https://doi.org/10.2969/jmsj/02830483

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Published: 1976 Received: June 10, 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: CITATION Details: Wrong : 1) R. Abraham, Foundations of Mechanics, Benjamin, 1967.
2) V. I. Arnold, On a characteristic class entering in Quantization conditions (translation), Functional Anal. Appl., 1 (1967), 1-13.
3) K. Asada and D. Fujiwara, On the boundedness of integral transformations with rapidly oscillatory kernels, submitted to J. Math. Soc. Japan.
4) G. D. Birkoff, Quantum mechanics and asymptotic series, Bull. Amer. Math. Soc., 39 (1933), 681-702.
5) R. Feynman, Space time approach to non relativistic quantum mechanics, Reviews of Modern Physics, 20 (1948), 368-387.
6) D. Fujiwara, Fundamental solution of partial differential operators of Schrödinger's type I, Proc. Japan Acad., 50 (1974), 566-569, and II, 699-701.
7) D. Fujiwara, On the boundedness of integral transformations with highly oscillatory kernels, Proc. Japan Acad., 51 (1975), 96-99.
8) L. Hörmander, Pseudo-differential operators, Comm. Pure Appl. Math., 18 (1965), 501-517.
9) L. Hörmander, Pseudo-differential operators and hypo-elliptic equations, Proc. Symp. Pure Math., 10 (1967), AMS.
10) L. Hörmander, Fourier integral operators I, Acta Math., 127 (1971), 79-183.
11) S. Kobayashi and K. Nomizu, Foundations of differential geometry 1, Interscience, 1963.
12) J. Leray, Solutions asymptotique des équations aux dérivées partielles, Séminaire des équations aux dérivées partielles de Collège de France, 1972.
13) J. Leray, Complément à la théorie d'Arnold de l'indice de Maslov, Séminaire des équations aux dérivées partielles de Collège de France, 1973.
14) V. P. Maslov, Théorie des perturbations et méthodes asymptotiques (translation), Dunod, 1972.

Right : [1] R. Abraham, Foundations of Mechanics, Benjamin, 1967.
[2] V. I. Arnold, On a characteristic class entering in Quantization conditions (translation), Functional Anal. Appl., 1 (1967), 1-13.
[3] K. Asada and D. Fujiwara, On the boundedness of integral transformations with rapidly oscillatory kernels, submitted to J. Math. Soc. Japan.
[4] G. D. Birkoff, Quantum mechanics and asymptotic series, Bull. Amer. Math. Soc., 39 (1933), 681-702.
[5] R. Feynman, Space time approach to non relativistic quantum mechanics, Reviews of Modern Physics, 20 (1948), 368-387.
[6] D. Fujiwara, Fundamental solution of partial differential operators of Schrödinger's type I, Proc. Japan Acad., 50 (1974), 566-569, and II, 699-701.
[7] D. Fujiwara, On the boundedness of integral transformations with highly oscillatory kernels, Proc. Japan Acad., 51 (1975), 96-99.
[8] L. Hörmander, Pseudo-differential operators, Comm. Pure Appl. Math., 18 (1965), 501-517.
[9] L. Hörmander, Pseudo-differential operators and hypo-elliptic equations, Proc. Symp. Pure Math., 10 (1967), AMS.
[10] L. Hörmander, Fourier integral operators I, Acta Math., 127 (1971), 79-183.
[11] S. Kobayashi and K. Nomizu, Foundations of differential geometry 1, Interscience, 1963.
[12] J. Leray, Solutions asymptotique des équations aux dérivées partielles, Séminaire des équations aux dérivées partielles de Collège de France, 1972.
[13] J. Leray, Complément à la théorie d'Arnold de l'indice de Maslov, Séminaire des équations aux dérivées partielles de Collège de France, 1973.
[14] V. P. Maslov, Théorie des perturbations et méthodes asymptotiques (translation), Dunod, 1972.

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

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