On holonomic systems for \(\prod_{l=1}^N(f_l+\sqrt{-1}0)^{\lambda_l}\). (English) Zbl 0449.35067


35N10 Overdetermined systems of PDEs with variable coefficients
35G05 Linear higher-order PDEs
35A99 General topics in partial differential equations
46F15 Hyperfunctions, analytic functionals
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
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[12] lagolnitzer, D., The u=Q structure theorem, Comm. math. Phys., 63 (1978), 49-96. Added in proof: The statement in page 9, line 4 is erroneous, because P/s and Qj’s do not satisfy the commutation relation. Hence the proof of Proposition 7 is not correct. Although the proof of Theorem 2 depends on Proposition 7, if we replace JTjt9 with -^O.pO^, £), it does not depend on Proposition 7. Here a= (ai, ●●●, ai), /9= (/?i, ●●●, &) eCl and Jfjt<f(ct,\() is obtained from J^s.9 by letting sj subject to the relation Sj-ajS+fij with one indeterminate s. Theorfore the proof of Theorem 18 is complete as it stands. The detailed corrections will be submitted to this journal. See also our paper "On the charac- teristic variety of a holonomic system with regular singularities," which will appear in Adv. in Math. It gives a complete proof for a generalization of Theorem 18.\)
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