A global representation of a fundamental set of solutions and a Stokes phenomenon for a system of linear ordinary differential equations

Kenjiro OKUBO

doi:10.2969/jmsj/01530268

Kenjiro OKUBO

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1963 Volume 15 Issue 3 Pages 268-288

DOI https://doi.org/10.2969/jmsj/01530268

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Published: 1963 Received: December 24, 1962 Available on J-STAGE: September 26, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 26, 2006 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) Tokyo metropolitan University

Right :
1) Tokyo Metropolitan University

Date of correction: September 26, 2006 Reason for correction: - Correction: CITATION Details: Right : [1] G. D. Birkhoff, [1] Collected mathematical papers.
[2] P. Diens, [1] Leçon sur les singularités des fonctions analytiques, 1913.
[3] W. B. Ford, [1] The asymptotic developments of functions defined by Maclaurin series, 1936.
[4] K. O. Friedrichs, [1] Special topics in analysis, 1955.
[5] J. Hadamard, [1] Essai sur l'étude de fonctions données par leur développement de Taylor, Partie III, Thèse, Paris, et J. de Math., 1892.
[6] J. Heading, [1] The Stokes phenomenon and certain n-th order differential equations, Proc. Cambridge Philos. Soc., 53 (1957), 399-441.
[7] L. Hopf, [1] Fortsetzungsrelationen bei der Lösungen der gewöhlichen linearer Differentialgleichungen, Math. Ann., 111 (1935), 679-712.
[8] E. L. Ince, [1] Ordinary differential equations, 1926.
[9] H. W. Knobloch, [1] Zusammenhänge zwischen konvergenten und asymptotischen Entwicklungen bei Lösungen linearer Differentialsystems von Range Eins, Math. Ann., 134 (1958), 260-288.
[10] R. E. Langer, [1] The solutions of the differential equation υ'''-λ²zυ'-3μλ²υ=0, Duke Math. J., 22 (1955), 525-541.
[11] P. Masani, [1] On a result of G. D. Birkhoff on linear differential systems, Proc. Amer. Math. Soc., 10 (1959), 696-698.
[12] N. E. Nörlund, [1] Leçon sur les séries d'interpolation, 1926.
[13] N. E. Nörlund, [2] Leçon sur les équations linéaires aux différences finies, 1929.
[14] H. L. Turrittin, [1] Stokes multipliers for a class of linear differential equations, Trans. Amer. Math. Soc., 68 (1950), 304-329.
[15] G. G. Stokes, [1] On the discontinuity of arbitrary constants which appear in divergent development, Trans. Cambridge Philos. Soc., 10 (1857), 106-128.
[16] E. M. Wright, [1] The asymptotic expansion of integral functions defined by Taylor series, Philos. Trans. Roy. Soc. London, Ser. A, 238 (1940), 423-451.

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