On the multisummability of WKB solutions of certain singularly perturbed linear ordinary differential equations

• Autorzy: Takei Y.

Identyfikatory

DOI

http://dx.doi.Org/10.7494/OpMath.2015.35.5.775

• Języki publikacji: EN

Abstrakty

EN

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

EN

exact WKB analysis; WKB solution; multisummability

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2015
• Tom: Vol. 35, no. 5
• Strony: 775--802
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Takei Y.

• RIMS, Kyoto University Kyoto 606-8502, Japan

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.