On the absolute summability factors of Fourier series at a given point
Fu Cheng Hsiang (1965-1966)
Compositio Mathematica
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Displaying similar documents to “Borel summability beyond the factorial growth”
On the absolute summability factors of Fourier series at a given point
On the summability of Fourier Series.
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We study a class of nonlinear difference equations admitting a -Gevrey formal power series solution which, in general, is not - (or Borel-) summable. Using right inverses of an associated difference operator on Banach spaces of so-called , we prove that this formal solution can be lifted to an analytic solution in a suitable domain of the complex plane and show that this analytic solution is an of the formal power series.