LAPLACE TRANSFORMS FOR ANALYTIC FUNCTIONS IN TUBULAR DOMAINS  

作　　者：Guantie DENG Qian FU Hui CAO 邓冠铁;付倩;曹辉(Laboratory of Mathematics and Complex Systems(Ministry of Education of China),School of Mathematical Sciences,Beijing Normal University,Beijing,100875,China)

机构地区：[1]Laboratory of Mathematics and Complex Systems(Ministry of Education of China),School of Mathematical Sciences,Beijing Normal University,Beijing,100875,China

出　　处：《Acta Mathematica Scientia》2021年第6期1938-1948,共11页数学物理学报（B辑英文版）

基　　金：This work was partially supported by NSFC(11971045,12071035 and 11971063).

摘　　要：Assume that 0<p<∞ and that B is a connected nonempty open set in R^(n),and that A^(p)(B)is the vector space of all holomorphic functions F in the tubular domains R^(n)+iB such that for any compact set K⊂B,‖ y →‖x →F(x+iy)‖Lp(R^(n))‖ L(K)<∞,so A^(p)(B)is a Frechet space with the Heine-Borel property,its topology is induced by a complete invariant metric,is not locally bounded,and hence is not normal.Furthermore,if 1≤p≤2,then the element F of A^(p)(B)can be written as a Laplace transform of some function f∈L(R^(n)).

关 键 词：Laplace transforms Fourier transform tubular domain regular cone 

分 类 号：O174[理学—数学]