Connection problems for asymptotic series
Author:
Wolfgang Wasow
Journal:
Bull. Amer. Math. Soc. 74 (1968), 831853
DOI:
https://doi.org/10.1090/S000299041968120555
MathSciNet review:
0228757
Fulltext PDF
References  Additional Information

G. D. Birkhoff [1933], Quantum mechanics and asymptotic series, Bull. Amer. Math. Soc. 32, 681700.

E. T. Copson [1965], Asymptotic expansions, Cambridge tracts in Mathematics and Mathematical Physics, no. 55, Cambridge Univ. Press, New York. MR 168979

M. A. Evgrafov, and M. B. Fedoryuk [1966], Asymptotic behavior of solutions of the equation w"(z) —p(z, λ)w(z) =0asλ → ∞ in the complex zplane, Uspehi Mat. Nauk 21, no. 1 (127) 350. (Russian)

W. B. Ford [1936], The asymptotic developments of functions defined by MacLaurin series, Univ. of Michigan Science Series, no. 11.

K. O. Friedrichs [1955], Asymptotic phenomena in mathematical physics, Bull. Amer. Math. Soc. 61, 485504. MR 74614

Nan Fröman, and P. O. Fröman [1965 ], JWKB approximation. Contributions to the theory, NorthHolland, Amsterdam. MR 173481

R. J. Hanson [1966], Reduction theorems for systems of ordinary differential equations with a turning point, J. Math. Anal. April. 16, 280301. MR 201748

R. J. Hanson [1968], Simplification of second order systems of ordinary differential equations with a turning point, (to appear). MR 244574

R. J. Hanson, and D. L. Russell [1967], Classification and reduction of second order systems at a turning point, J. Math, and Phys. 46, 7492. MR 208097

P.F. Hsieh and Y. Sibuya [1966], On the asymptotic integration of second order linear ordinary differential equations with polynomial coefficients, J. Math. Anal. Appl. 16, 84103. MR 200512

H. K. Hughes [1945 ] The asymptotic developments of a class of entire functions, Bull. Amer. Math. Soc. 51, 456461. MR 12132

M. Iwano [1963] Asymptotic solutions of a system of linear ordinary differential equations containing a small parameter. I, Funkcial. Ekvac. 5, 71134. MR 171045

M. Iwano and Y. Sibuya [1963], Reduction of the order of a linear ordinary differential equation containing a small parameter, Kōdai Math. Sem. Rep. 15, 128. MR 149034

K. Kiyek [1967], Über eine spezielle Klasse linearer Differentialsysteme mit einem kleinen Parameter, Arch. Rational Mech. Anal. 25, 135147. MR 213661

R. Langer [1934], The asymptotic solutions of ordinary linear differential equations with special reference to the Stokes phenomenon, Bull. Amer. Math. Soc. 40, 545582.

Roy Lee [1967], Asymptotic analysis of solutions of almost diagonal systems of ordinary differential equations at a turning point, Thesis, University of Wisconsin, Madison, Wis.

T. Nishimoto [1965a], On matching methods in turning point problems, Kōdai Math. Sem. Rep. 17, 198221. MR 183945

T. Nishimoto [1965b], [1966], [1967], On matching methods for a linear ordinary differential equation containing a parameter. I, II, III, Kōdai Math. Sem. Rep. 17, 307328; ibid., 18, 6186; ibid., 19, 8094.

T. Okubo [1966], On certain reduction theorems for systems of differential equations which contain a turning point, Proc. Japan Acad. 9, 544549. MR 138826

T. Okubo [1966], A global representation of a fundamental set of solutions and a Stokes phenomenon for a system of linear ordinary differential equations, J. Math. Soc. Japan 15, 268288. MR 156025

K. Okubo [1965], A connection problem involving a logarithmic function, Publ. Res. Inst. Math. Sci. Ser. A 1, 99128. MR 185202

F. W. J. Olver [1965], Error analysis of phaseintegral methods. I: General theory for simple turning points; II. Applications to wavepenetration problems, J. Res. Nat. Bur. Standards Sect. B 69B, 271290; ibid., 291300. MR 196167

Y. Sibuya [1962], Asymptotic solutions of a system of linear ordinary differential equations containing a parameter, Funkcial. Ekvac. 4, 83113. MR 141853

Y. Sibuya [1967], Subdominant solutions of the differential equation y"—λ(x—a_{1}) (x—a_{2}) • • • (xa_{m})y=0.

G. Stengle [1961 ], A construction for solutions of an nth order linear differential equation in the neighborhood of a turning point, Ph.D. Thesis, Univ. Wisconsin, Madison, Wis.

G. Stengle [1964], Asymptotic solution of a class of second order differential equations containing a parameter, Report IMMNYU 319, New York Univ., Courant Inst. of Math. Sciences, New York.

H. L. Turrittin [1950], Stokes multipliers for asymptotic solutions of a certain differential equation, Trans. Amer. Math. Soc. 68, 304329. MR 34491

W. Wasow [1961], Turning point problems for systems of linear equations. I : The formal theory, Comm. Pure Appl. Math. 14, 657673. MR 132248

W. Wasow [1962], Turning point problems for systems of linear differential equations. II: The analytic theory, Comm. Pure Appl. Math. 15, 173187. MR 146466

W. Wasow [1963], Simplification of turning point problems for systems of linear differential equations, Trans. Amer. Math. Soc. 106, 100114. MR 142836

W. Wasow [1965], Asymptotic expansions for ordinary differential equations, Pure and Appl. Math., vol. 14, Interscience, New York. MR 203188

W. Wasow [1966a], On turning point problems for systems with almost diagonal coefficient matrix, Funkcial. Ekvac. 8, 143171. MR 200558

W. Wasow [1966b], [1967], On the analytic validity of formal simplifications of linear differential equations. I, Funkcial. Ekvac. 9, 8391; II, Funkcial. Ekvac. 10, 107122. MR 212305
Additional Information
DOI:
https://doi.org/10.1090/S000299041968120555