Abstract
Smoothness of aC ∞-functionf is measured by (Carleman) sequence {M k} ∞0 ; we sayf∈C ∞ M [0, 1] if|f (k) (t)|≤CR k M k,k=0, 1, ... withC, R>0. A typical statement proven in this paper isTHEOREM: Let u, b be two C ∞ -functions on [0, 1]such that (a) u′=u 2+b, (b) |b (k) (t)|≤CR k (k!) γ, γ>1,k∈ℤ−.Then |u(k)(t)|≤C1Rk((k−1)!)γ,k∈ℤ−.
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The first author acknowledges the hospitality of Mathematical Research Institute of the Ohio State University during his one month visit there in the spring of 1999
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Djakov, P., Mityagin, B. Smoothness of solutions of a nonlinear ode. Integr equ oper theory 44, 149–171 (2002). https://doi.org/10.1007/BF01217531
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DOI: https://doi.org/10.1007/BF01217531