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• W2167723732 abstract "Let L = ∑ i = 1 d X i ( z ) ∂ z i be a holomorphic vector field degenerating at z = 0 such that Jacobi matrix ( ( ∂ X i / ∂ z j ) ( 0 ) ) has zero eigenvalues. Consider L u = F ( z , u ) and let u ˜ ( z ) be a formal power series solution. We study the Borel summability of u ˜ ( z ) , which implies the existence of a genuine solution u ( z ) such that u ( z ) ∼ u ˜ ( z ) as z → 0 in some sectorial region. Further we treat singular equations appearing in finding normal forms of singular vector fields and study to simplify L by transformations with Borel summable functions." @default.
• W2167723732 created "2016-06-24" @default.
• W2167723732 creator A5045661231 @default.
• W2167723732 date "2005-04-01" @default.
• W2167723732 modified "2023-10-16" @default.
• W2167723732 title "Borel summability of formal solutions of some first order singular partial differential equations and normal forms of vector fields" @default.
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• W2167723732 doi "https://doi.org/10.2969/jmsj/1158242065" @default.
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