Shifts-invariant spaces in L 1(R) are investigated. First,based on a study of the system of linearly difference operators,the method of constructing generators with linearly independent shifts is provided. Then the c...Shifts-invariant spaces in L 1(R) are investigated. First,based on a study of the system of linearly difference operators,the method of constructing generators with linearly independent shifts is provided. Then the characterizations of the closed shift-invariant subspaces in L 1(R) are given in terms of such generators and the local basis of shift-invariant subspaces.展开更多
Given a doubling weightωon the unit disk D,let A_(ω)^(p) be the space of all the holomorphic functions f,where∥f∥A_(ω)^(p):=(∫_(D)|f(z)|_(p)ω(z)dA(z))^(1/p)<∞.We completely characterize the topological conn...Given a doubling weightωon the unit disk D,let A_(ω)^(p) be the space of all the holomorphic functions f,where∥f∥A_(ω)^(p):=(∫_(D)|f(z)|_(p)ω(z)dA(z))^(1/p)<∞.We completely characterize the topological connectedness of the set of composition operators on A_(ω)^(p).As an application,we construct an interesting example which reveals that two composition operators on A_(α)^(p) in the same path component may fail to have a compact difference and give a negative answer to the Shapiro-Sundberg question in the(standard)weighted Bergman space.In addition,we completely describe the central compactness of any finite linear combinations of composition operators on A_(ω)^(p) in three terms:a Julia-Carathéodory-type function-theoretic characterization,a power-type characterization,and a Carleson-type measure-theoretic characterization.展开更多
基金the National Natural Science Foundation of China(1 0 0 71 0 71 )
文摘Shifts-invariant spaces in L 1(R) are investigated. First,based on a study of the system of linearly difference operators,the method of constructing generators with linearly independent shifts is provided. Then the characterizations of the closed shift-invariant subspaces in L 1(R) are given in terms of such generators and the local basis of shift-invariant subspaces.
基金supported by National Natural Science Foundation of China (Grant Nos. 12101467 and 12171373)。
文摘Given a doubling weightωon the unit disk D,let A_(ω)^(p) be the space of all the holomorphic functions f,where∥f∥A_(ω)^(p):=(∫_(D)|f(z)|_(p)ω(z)dA(z))^(1/p)<∞.We completely characterize the topological connectedness of the set of composition operators on A_(ω)^(p).As an application,we construct an interesting example which reveals that two composition operators on A_(α)^(p) in the same path component may fail to have a compact difference and give a negative answer to the Shapiro-Sundberg question in the(standard)weighted Bergman space.In addition,we completely describe the central compactness of any finite linear combinations of composition operators on A_(ω)^(p) in three terms:a Julia-Carathéodory-type function-theoretic characterization,a power-type characterization,and a Carleson-type measure-theoretic characterization.
