The aim of this paper is to establish an extension of qualitative and quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator.
In this paper, we show that for log(2/3)/2log2≤ β ≤1/2, suppose S is an invariant subspace of the Hardy-Sobolev spaces H_β~2(D^n) for the n-tuple of multiplication operators(M_(z_1),...,M_(z_n)). If(M_(z_1)|S,...,...In this paper, we show that for log(2/3)/2log2≤ β ≤1/2, suppose S is an invariant subspace of the Hardy-Sobolev spaces H_β~2(D^n) for the n-tuple of multiplication operators(M_(z_1),...,M_(z_n)). If(M_(z_1)|S,..., M_(z_n)|S) is doubly commuting, then for any non-empty subset α = {α_1,..., α_k} of {1,..., n}, W_α~S is a generating wandering subspace for M_α|_S =(M_(z_(α_1))|_S,..., M_(z_(α_k))|_S), that is, [W_α~S]_(M_(α |S))= S, where W_α~S=■(S ■ z_(α_i)S).展开更多
In this paper, we prove that for -1/2≤β≤0, suppose M is an invariant subspaces of the Hardy Sobolev spaces Hβ^2（D） for Tz^β, then M zM is a generating wandering subspace of M, that is, M = [M zM]Tz^β. More...In this paper, we prove that for -1/2≤β≤0, suppose M is an invariant subspaces of the Hardy Sobolev spaces Hβ^2（D） for Tz^β, then M zM is a generating wandering subspace of M, that is, M = [M zM]Tz^β. Moreover, any non-trivial invariant subspace M of Hβ^2（D） is also generated by the quasi-wandering subspace PMTz^βM^⊥, that is, M = [PMTz^βM^⊥]Tz^β.展开更多
Let H^2(γ) be the Hilbert space over the bidisk D^2 generated by a positive sequence γ={γnm}n,m≥0. In this paper, we prove that the Beurling type theorem holds for the shift operator on H^2(γ) with γ={γnm}n,m≥...Let H^2(γ) be the Hilbert space over the bidisk D^2 generated by a positive sequence γ={γnm}n,m≥0. In this paper, we prove that the Beurling type theorem holds for the shift operator on H^2(γ) with γ={γnm}n,m≥0 satisfying certain series of inequalities. As a corollary, we give several applications to a class of classical analytic reproducing kernel Hilbert spaces over the bidisk D^2.展开更多
文摘The aim of this paper is to establish an extension of qualitative and quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator.
基金supported by the Natural Science Foundation of China(11271092,11471143)the key research project of Nanhu College of Jiaxing University(N41472001-18)
文摘In this paper, we show that for log(2/3)/2log2≤ β ≤1/2, suppose S is an invariant subspace of the Hardy-Sobolev spaces H_β~2(D^n) for the n-tuple of multiplication operators(M_(z_1),...,M_(z_n)). If(M_(z_1)|S,..., M_(z_n)|S) is doubly commuting, then for any non-empty subset α = {α_1,..., α_k} of {1,..., n}, W_α~S is a generating wandering subspace for M_α|_S =(M_(z_(α_1))|_S,..., M_(z_(α_k))|_S), that is, [W_α~S]_(M_(α |S))= S, where W_α~S=■(S ■ z_(α_i)S).
基金Project 10871003 supported-by National Natural Science Foundation of Chinathe Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20030001107)
文摘In this paper, we prove Beurling＇s theorem for the Jacobi transform, from which we derive some other versions of uncertainty principles.
基金Supported by National Natural Science Foundation of China(Grant No.11671152)the key research project of Nanhu College of Jiaxing University(Grant.No.N41472001-18)
文摘In this paper, we prove that for -1/2≤β≤0, suppose M is an invariant subspaces of the Hardy Sobolev spaces Hβ^2（D） for Tz^β, then M zM is a generating wandering subspace of M, that is, M = [M zM]Tz^β. Moreover, any non-trivial invariant subspace M of Hβ^2（D） is also generated by the quasi-wandering subspace PMTz^βM^⊥, that is, M = [PMTz^βM^⊥]Tz^β.
基金Supported by NSFC(Grant Nos.11271332 and 11431011)the Fundamental Research Funds for the Central UniversitiesNSFC(Grant No.11501249)
文摘Let H^2(γ) be the Hilbert space over the bidisk D^2 generated by a positive sequence γ={γnm}n,m≥0. In this paper, we prove that the Beurling type theorem holds for the shift operator on H^2(γ) with γ={γnm}n,m≥0 satisfying certain series of inequalities. As a corollary, we give several applications to a class of classical analytic reproducing kernel Hilbert spaces over the bidisk D^2.
