On the Fourier-Laplace transform of functionals on a space of infinitely differentiable functions on a convex compact
Journal of Mathematical Analysis and Applications(2022)
摘要
Classes of ultradifferentiable functions are classically defined by imposing growth conditions on the derivatives of the functions. Following this approach we consider a Fréchet-Schwartz space of infinitely differentiable functions on a closure of a bounded convex domain of multidimensional real space with uniform bounds on their partial derivatives. Our aim is to obtain Paley-Wiener-Schwartz type theorem connecting properties of linear continuous functionals on this space with the behaviour of their Fourier-Laplace transforms. Very similar problems were considered by M. Neymark, B.A. Taylor, M. Langenbruch, A.V. Abanin.
更多查看译文
关键词
Ultradifferentiable functions,Dual space,Fourier-Laplace transformation of functionals,Entire functions,Young-Fenchel transform
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要