By Masaki Kashiwara, Takahiro Kawai
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Extra info for Algebraic Analysis. Papers Dedicated to Professor Mikio Sato on the Occasion of his Sixtieth Birthday, Volume 1
One may easily imagine that one can develop a similar theory of maximally overdetermined, namely holonomic, systems of g-difference equations. In recent years there has been consider able interest in the g-analog of special functions such as g-basic series and their extensions (see [A2], [ M l ] , [M2], etc). It seems that these are intimately related to holonomic ^-difference systems. C. Praagman has investigated n commuting linear difference operators including (2) below, at least in formal series settings (see [P]).
30 (1929) 195-205. [A2] G. Andrews, Problems and prospects for basic hypergeometric functions, in Theory and Application of Special Functions (R. ), pp. 191-224, Academic Press, New York, 1975. [A3] K. Aomoto, Les équations aux differences linéaires et les integrales des fonctions multiformes, J. Fac. Sci. Univ. Tokyo 22 (1975) 271-297. [B] G. D. Birkhoff, The generalized Riemann problem for linear differential and the allied problems for linear difference and q-difference equations, Proc. Am. Acad.
Math. 3 (1954) 57-122.  R. Ishimura, Théorèmes d'existence et d'approximation pour les équations aux dérivées partielles linéaires d'ordre infini, Pubi. RIMS, Kyoto Univ. 16 (1980) 393-415.  R. Ishimura, Existence locale de solutions holomorphes pour les équations différentiels d'ordre infini, Ann. Inst. Fourier, Grenoble 35-3 (1985) 49-57.  M. Kashiwara and T. Kawai, On holonomic systems of microdifferential equations, III. Pubi. , 17 (1981) 813-979.  M. Kashiwara and P. Schapira, Micro-hyperbolic systems, Acta Mathematica 142 (1979) 1-55.
Algebraic Analysis. Papers Dedicated to Professor Mikio Sato on the Occasion of his Sixtieth Birthday, Volume 1 by Masaki Kashiwara, Takahiro Kawai