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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

The meaning of Maslov's asymptotic method: The need of Planck's constant in mathematics


Author: Jean Leray
Journal: Bull. Amer. Math. Soc. 5 (1981), 15-27
MSC (1980): Primary 47B99, 81C99; Secondary 35S99, 42B99
MathSciNet review: 614311
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References [Enhancements On Off] (What's this?)

  • 1. V. I. Arnol′d, On a characteristic class entering into conditions of quantization, Funkcional. Anal. i Priložen. 1 (1967), 1–14 (Russian). MR 0211415 (35 #2296)
  • 2. V. S. Buslaev, Quantization and the WKB method, Trudy Mat. Inst. Steklov. 110 (1970), 5–28 (Russian). MR 0297258 (45 #6315)
  • 3. V. P. Maslov, Perturbation theory and asymptotic methods, M. G. U., Moscow, 1965. (Russian)
  • 4. H. Poincaré, Sur les intégrales irrégulières, Acta Math. 8 (1886), no. 1, 295–344 (French). Des équations linéaires. MR 1554701, http://dx.doi.org/10.1007/BF02417092
  • 5. I. E. Segal, Foundations of the theory of dynamical systems of infinitely many degrees of freedom. I, Mat.-Fys. Medd. Danske Vid. Selsk. 31 (1959), no. 12, 39 pp. (1959). MR 0112626 (22 #3477)
  • 6. Jean Leray, Analyse lagrangienne et mécanique quantique, Séminaire sur les Équations aux Dérivées Partielles (1976–1977), I, Collège de France, Paris, 1977, pp. Exp. No. 1, 303 (French). MR 0501198 (58 #18617)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0273-0979-1981-14914-4
PII: S 0273-0979(1981)14914-4