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On the radius of analyticity of solutions to the cubic Szego equation


This paper is concerned with the cubic Szego equationi {equation presented}, defined on the L2 Hardy space on the one-dimensional torus T, where π : L2(T)→L2+(T) is the Szego projector onto the non-negative frequencies. For analytic initial data, it is shown that the solution remains spatial analytic for all time t ∈(-infin;,∞). In addition, we find a lower bound for the radius of analyticity of the solution. Our method involves energy-like estimates of the special Gevrey class of analytic functions based on the l1 norm of Fourier transforms (the Wiener algebra).

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