no. 3
On meromorphic equivalence of linear difference operators
Annales de l'Institut Fourier, Tome 40 (1990) no. 3, pp. 683-699.

On étudie des équations linéaires aux différences finies à coefficients méromorphes à l’infini. On caractérise les classes d’équivalence méromorphes de telles équations par un système d’invariants méromorphes. On démontre la liberté de ce systèmes en utilisant une méthode inspirée des travaux de G.D. Birkhoff.

We consider linear difference equations whose coefficients are meromorphic at ∞. We characterize the meromorphic equivalence classes of such equations by means of a system of meromorphic invariants. Using an approach inspired by the work of G. D. Birkhoff we show that this system is free.

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Immink, Gertrude K. On meromorphic equivalence of linear difference operators. Annales de l'Institut Fourier, Tome 40 (1990) no. 3, pp. 683-699. doi : 10.5802/aif.1228. http://www.numdam.org/articles/10.5802/aif.1228/

[1] G.D. Birkhoff, The generalized Riemann problem for linear differential equations and the allied problems for linear difference and q-difference equations, Proc. Amer. Acad. Arts and Sci., 49 (1913), 521-568. | JFM

[2] G.D. Birkhoff and W.J. Trjitzinsky, Analytic theory of linear difference equations, Acta Math., 60 (1933), 1-89. | JFM | Zbl

[3] J. Ecalle, Les fonctions résurgentes, t. III, Publ. Math. d'Orsay, Université de Paris-Sud (1985).

[4] A.S. Fokas and M.J. Ablowitz, On the initial value problem of the second Painlevé transcendent, Comm. Math. Phys., 91 (1983), 381-403. | MR | Zbl

[5] G.K. Immink, Reduction to canonical forms and the Stokes phenomenon in the theory of linear difference equations, To appear in SIAM J. Math. Anal., 22 (1991). | MR | Zbl

[6] G.K. Immink, On the asymptotic behaviour of the coefficients of asymptotic power series and its relevance to Stokes phenomena, To appear in SIAM J. Math. Anal., 22 (1991). | Zbl

[7] W.B. Jurkat, Meromorphe Differentialgleichungen, Lecture Notes in Mathematics 637, Springer Verlag, Berlin (1978). | MR | Zbl

[8] B. Malgrange, Remarques sur les équations différentielles à points singuliers irréguliers, In : Equations différentielles et systèmes de Pfaff dans le champ complexe, Lecture Notes in Mathematics, 712 (1979), 77-86. | MR | Zbl

[9] N.I. Muskhelishvili, Singular integral equations, Noordhoff, Groningen, 1953.

[10] C. Praagman, The formal classification of linear difference operators, Proc. Kon. Ned. Ac. Wet. Ser. A, 86 (1983), 249-261. | MR | Zbl

[11] Y. Sibuya, Stokes phenomena, Bull. Amer. Math. Soc., 83 (1977), 1075-1077. | MR | Zbl

[12] E.C. Titchmarsh, The theory of functions (2nd ed.), Oxford University Press, Oxford, 1939. | JFM

[13] N.P. Vekua, Systems of singular integral equations, Gordon and Breach, New York, 1967.

[14] J. Martinet, J.P. Ramis, Problèmes de modules pour des équations différentielles non linéaires du premier ordre, Publ. Math. IHES, 55 (1982), 63-162. | Numdam | MR | Zbl

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