Abstract
The author reviews briefly the classical theory of homogeneous solutions of linear ordinary differential equations near an irregular singular point and its application to the existence of ultradistribution solutions of Gevrey classes. Then he develops an analogous theory for formal solutions of linear partial differential equations near a characteristic surface of constant multiplicity. As a consequence he shows that the irregularity condition he introduced earlier in [13] and [14] is necessary in general in order that a formally hyperbolic equation with real analytic coefficients be well posed in a corresponding Gevrey class of functions and ultradistributions.
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Komatsu, H. (1986). The Necessity of the Irregularity Condition for Solvability in Gevrey Classes (s) and {s}. In: Garnir, H.G. (eds) Advances in Microlocal Analysis. NATO ASI Series, vol 168. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4606-4_6
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DOI: https://doi.org/10.1007/978-94-009-4606-4_6
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