FOURIER COEFFICIENTS OF PERIODIC FUNCTIONS OF GEVREY CLASSES AND ULTRADISTRIBUTIONS
FOURIER COEFFICIENTS OF PERIODIC FUNCTIONS OF GEVREY CLASSES AND ULTRADISTRIBUTIONS
复制标题
DOI：
--
复制
发表时间：
1987
期刊：
影响因子：
--
通讯作者：
Yoshiko Taguchi
中科院分区：
文献类型：
--
作者：
Yoshiko Taguchi
S（s>1）型开域R“上的超可微函数类及其对偶空间的Gevrey类是H. Komatsu（[1]，[2]）.在单点支集的情况下，J. P. Ramis（[7]，[8]）研究了$s（-\infty<s<+\infty）$型函数的Gevrey类。从定义中可以知道，对于$s\leq 1$，这些函数是解析的，因此通常的泛函分析技术就失效了。这就是为什么Ramis使用正式的幂级数来克服其中的一些困难。本文研究了单位圆T$上s（-\infty<s<+\infty）$型超可微函数的Gevrey类.我们的特征在于这些功能的增长条件的傅立叶系数。事实证明，对于$s<0$，超可微函数只是常数函数，但我们确实有$s\leq 1$的解析情况。由于空间T是紧的，我们仍然可以用泛函分析的方法来定义和估计对偶元素的Fourier系数
Gevrey classes of ultradifferentiable functions on an open domain $\Omega\subset R$ “ 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 $s\leq 1$ , 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 $s\leq 1$ . 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