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.
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.
@article{AIF_1990__40_3_683_0, author = {Immink, Gertrude K.}, title = {On meromorphic equivalence of linear difference operators}, journal = {Annales de l'Institut Fourier}, pages = {683--699}, publisher = {Imprimerie Louis-Jean}, address = {Gap}, volume = {40}, number = {3}, year = {1990}, doi = {10.5802/aif.1228}, mrnumber = {92e:39018}, zbl = {0697.39006}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1228/} }
TY - JOUR TI - On meromorphic equivalence of linear difference operators JO - Annales de l'Institut Fourier PY - 1990 DA - 1990/// SP - 683 EP - 699 VL - 40 IS - 3 PB - Imprimerie Louis-Jean PP - Gap UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1228/ UR - https://www.ams.org/mathscinet-getitem?mr=92e:39018 UR - https://zbmath.org/?q=an%3A0697.39006 UR - https://doi.org/10.5802/aif.1228 DO - 10.5802/aif.1228 LA - en ID - AIF_1990__40_3_683_0 ER -
Immink, Gertrude K. On meromorphic equivalence of linear difference operators. Annales de l'Institut Fourier, Volume 40 (1990) no. 3, pp. 683-699. doi : 10.5802/aif.1228. https://aif.centre-mersenne.org/articles/10.5802/aif.1228/
[1] 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: 44.0391.03
,[2] Analytic theory of linear difference equations, Acta Math., 60 (1933), 1-89. | JFM: 59.0450.03 | Zbl: 0006.16802
and ,[3] Les fonctions résurgentes, t. III, Publ. Math. d'Orsay, Université de Paris-Sud (1985).
,[4] On the initial value problem of the second Painlevé transcendent, Comm. Math. Phys., 91 (1983), 381-403. | MR: 86b:34011 | Zbl: 0524.35094
and ,[5] 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: 92c:39005 | Zbl: 0733.39004
,[6] 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: 0716.30032
,[7] Meromorphe Differentialgleichungen, Lecture Notes in Mathematics 637, Springer Verlag, Berlin (1978). | MR: 82a:34004 | Zbl: 0408.34004
,[8] 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: 80k:14019 | Zbl: 0423.32014
,[9] Singular integral equations, Noordhoff, Groningen, 1953.
,[10] The formal classification of linear difference operators, Proc. Kon. Ned. Ac. Wet. Ser. A, 86 (1983), 249-261. | MR: 85c:12006 | Zbl: 0519.39003
,[11] Stokes phenomena, Bull. Amer. Math. Soc., 83 (1977), 1075-1077. | MR: 56 #720 | Zbl: 0386.34008
,[12] The theory of functions (2nd ed.), Oxford University Press, Oxford, 1939. | JFM: 65.0302.01
,[13] Systems of singular integral equations, Gordon and Breach, New York, 1967.
,[14] Problèmes de modules pour des équations différentielles non linéaires du premier ordre, Publ. Math. IHES, 55 (1982), 63-162. | Numdam | MR: 84k:34011 | Zbl: 0546.58038
, ,Cited by Sources: