关于双向加细方程的L^1-解的一点注记  

A note on L^1-solutions of two-direction refinement equations

作　　者：延卫军[1] 

机构地区：[1]榆林学院数学系,陕西榆林719000

出　　处：《纺织高校基础科学学报》2011年第4期469-472,498,共5页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金资助项目(10571113);榆林学院高层次人才科研启动基金(11GK63)

摘　　要：研究了双向加细方程f(x)=sum(c(n,1)f(αx-β_n))from n=0 to N+sum(c(n,-1)f(-αx-β_n))from n=0 to N的L1-解,其中α∈R且α>1,β0<…<βN∈R.利用傅里叶方法和迭代函数系将证明双向加细方程的所有L1-解所做成的解空间至少是1维的,并且给出了双向加细方程非平凡L1-解存在的充分条件与必要条件,同时给出非平凡L1-解不存在的条件,所得结果容易验证.L1-solutions of the following two-direction refinement equations is studied：f（x）=sum（c（n,1）f（αx-β_n））from n=0 to N＋sum（c（n,-1）f（-αx-β_n））from n=0 to N, where α are constant real number and α1,β0…βN are also real numbers.It was proved that the vector space of all L1-solutions of the above equation is at most 1-dimensional by the Fourier techniques and iterated function systems.The sufficient and necessary conditions for the existence of nontrivial L1-solutions of the two-direction refinement equation as well as for the nonexistence of such solutions are given.Moreover,it is easy for verification.

关 键 词：双向加细方程 傅里叶方法 迭代函数系 L1-解 

分 类 号：O174.2[理学—数学]