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Sep 22, 2023 at 15:50 comment added Erik Lundberg The reference to Hormander provided by user80744 is a good one. For your second question, if I understand correctly, the answer is "no", unless you also assume some lower bound on the radius of convergence of the data in the sequence (and then you get an estimate on the size of the domain of the corresponding sequence of solutions not from the assumption about what the data approximate but rather from applying C-K at each step of the sequence). If you clarify your question by indicating whether you want to assume lower bound on radius of convergence of each data function, I can elaborate.
Aug 24, 2018 at 20:54 answer added user80744 timeline score: 3
Aug 22, 2018 at 0:33 history edited RBega2 CC BY-SA 4.0
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Aug 21, 2018 at 23:59 history asked RBega2 CC BY-SA 4.0