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Języki publikacji
Abstrakty
Using two concrete examples, we discuss the multisummability of WKB solutions of singularly perturbed linear ordinary differential equations. Integral representations of solutions and a criterion for the multisummability based on the Cauchy-Heine transform play an important role in the proof.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
775--802
Opis fizyczny
Bibliogr. 10 poz., rys.
Twórcy
Bibliografia
- [1] W. Balser, From Divergent Power Series to Analytic Functions, Lecture Notes in Mathematics, vol. 1582, Springer-Verlag, 1994.
- [2] S. Bodine, R. Schafke, On the summability of formal solutions in Liouville-Green theory, J. Dynam. Control Systems 8 (2002), 371-398.
- [3] E. Delabaere, F. Pham, Resurgent methods in semi-classical asymptotics, Ann. Inst. H. Poincare 71 (1999), 1-94.
- [4] T.M. Dunster, D.A. Lutz, R. Schafke, Convergent Liouville-Green expansions for second-order linear differential equations, with an application to Bessel functions, Proc. Roy. Soc. London, Ser. A 440 (1993), 37-54.
- [5] T. Kawai, Y. Takei, Algebraic Analysis of Singular Perturbation Theory, Translations of Mathematical Monographs, Vol. 227, Amer. Math. Soc, 2005.
- [6] T. Koike, R. Schafke, On the Borel summability of WKB solutions of Schrodinger equations with polynomial potentials and its applications, in preparation.
- [7] R. Schafke, private communication.
- [8] K. Suzuki, On multisummable WKB solutions of a certain ordinary differential equation of singular perturbation type, Master-thesis, Kyoto University, 2012.
- [9] K. Suzuki, Y. Takei, Exact WKB analysis and multisummability - A case study -, RIMS Kokyuroku 1861 (2013), 146-155.
- [10] A. Voros, The return of the quartic oscillator. The complex WKB method, Ann. Inst. H. Poincare 39 (1983), 211-338.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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