On quasianalytic classes of functions, expansible in series

Analyticity of Solutions for a Generalized Euler Equation

“…For fixed t=t 0 , the radius of the space-time ball of analyticity depends only on the radius of the ball of spatial analyticity [20]. It is uniform in the spatial variables because |(t 0 , } ) is in a Gevrey class, and uniform for all t 0 # [0, T] through estimate (22). This implies global analyticity in time as well as space, whereby we have established the following theorem.…”

“…For example, one can first construct local analytic solutions in D(A r e {(t) A ) as the limit of a Fourier Galerkin approximating sequence, and then globalize the result by estimate (22). This shows that…”

“…In fact, they are special cases of the quasianalytic classes which had been introduced earlier by Hadamard [19]. La Valle e Poussin [23] showed that, among the quasianalytic functions, the Gevrey classes are characterized by an exponential decay of their Fourier coefficients (see also [22]). In turn, this characterization has recently proved useful for showing that the solutions of various nonlinear partial differential equations are analytic.…”