On meromorphic equivalence of linear difference operators

Gertrude K. Immink

Annales de l'institut Fourier (1990)

  • Volume: 40, Issue: 3, page 683-699
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Immink, Gertrude K.. "On meromorphic equivalence of linear difference operators." Annales de l'institut Fourier 40.3 (1990): 683-699. <http://eudml.org/doc/74892>.

@article{Immink1990,
abstract = {We consider linear difference equations whose coefficients are meromorphic at $\infty $. 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.},
author = {Immink, Gertrude K.},
journal = {Annales de l'institut Fourier},
keywords = {linear difference operator; formal equivalence; inverse problem; Riemann- Hilbert problem; linear difference equations; meromorphic equivalence; meromorphic invariants},
language = {eng},
number = {3},
pages = {683-699},
publisher = {Association des Annales de l'Institut Fourier},
title = {On meromorphic equivalence of linear difference operators},
url = {http://eudml.org/doc/74892},
volume = {40},
year = {1990},
}

TY - JOUR
AU - Immink, Gertrude K.
TI - On meromorphic equivalence of linear difference operators
JO - Annales de l'institut Fourier
PY - 1990
PB - Association des Annales de l'Institut Fourier
VL - 40
IS - 3
SP - 683
EP - 699
AB - We consider linear difference equations whose coefficients are meromorphic at $\infty $. 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.
LA - eng
KW - linear difference operator; formal equivalence; inverse problem; Riemann- Hilbert problem; linear difference equations; meromorphic equivalence; meromorphic invariants
UR - http://eudml.org/doc/74892
ER -

References

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  1. [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. Zbl44.0391.03JFM44.0391.03
  2. [2] G.D. BIRKHOFF and W.J. TRJITZINSKY, Analytic theory of linear difference equations, Acta Math., 60 (1933), 1-89. Zbl0006.16802JFM59.0450.03
  3. [3] J. ECALLE, Les fonctions résurgentes, t. III, Publ. Math. d'Orsay, Université de Paris-Sud (1985). 
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  5. [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). Zbl0733.39004MR92c:39005
  6. [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). Zbl0716.30032
  7. [7] W.B. JURKAT, Meromorphe Differentialgleichungen, Lecture Notes in Mathematics 637, Springer Verlag, Berlin (1978). Zbl0408.34004MR82a:34004
  8. [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. Zbl0423.32014MR80k:14019
  9. [9] N.I. MUSKHELISHVILI, Singular integral equations, Noordhoff, Groningen, 1953. 
  10. [10] C. PRAAGMAN, The formal classification of linear difference operators, Proc. Kon. Ned. Ac. Wet. Ser. A, 86 (1983), 249-261. Zbl0519.39003MR85c:12006
  11. [11] Y. SIBUYA, Stokes phenomena, Bull. Amer. Math. Soc., 83 (1977), 1075-1077. Zbl0386.34008MR56 #720
  12. [12] E.C. TITCHMARSH, The theory of functions (2nd ed.), Oxford University Press, Oxford, 1939. Zbl0022.14602JFM65.0302.01
  13. [13] N.P. VEKUA, Systems of singular integral equations, Gordon and Breach, New York, 1967. Zbl0166.09802
  14. [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. Zbl0546.58038MR84k:34011

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