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- W151136944 abstract "Gevrey classes of ultradifferentiable functions on an open domain $Omegasubset R$ “ of type $s(s>1)$ and their dual spaces are extensively studied by Professor H. Komatsu ([1], [2]). In the case of one point support, J. P. Ramis ([7], [8]) has studied Gevrey classes of functions of type $s(-infty<s<+infty)$ . It is known from the definition that for $sleq 1$ , these functions are analytic so that the usual technique of functional analysis breaks down. That is why Ramis uses formal power series to overcome some of these difficulties. In this paper, we study Gevrey classes of ultradifferentiable functions of type $s(-infty<s<+infty)$ on the unit circle $T$ . We characterize these functions by growth conditions on their Fourier coefficients. It turns out that for $s<0$, ultradifferentiable functions are only constant functions but we do have analytic cases for $sleq 1$ . Since the space $T$ is compact, we can still use the method of functional analysis to define and estimate the Fourier coefficients of dual elements" @default.
- W151136944 created "2016-06-24" @default.
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- W151136944 date "1987-01-01" @default.
- W151136944 modified "2023-09-23" @default.
- W151136944 title "FOURIER COEFFICIENTS OF PERIODIC FUNCTIONS OF GEVREY CLASSES AND ULTRADISTRIBUTIONS" @default.
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