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- W2044638023 abstract "Abstract Let ω be a weight on Z and assume that the spectrum of the usual shift operator on the weighted space l ω 2 ( Z ) equals the unit circle. We show that if ∑ n log ω(n) n 2 =+∞ , and if the sequence (ω(−n))n⩾0 satisfies suitable growth and regularity conditions, then all nontrivial translation invariant subspaces of l ω 2 ( Z ) are generated by their intersection with l ω 2 ( Z + )= u=(u n ) n∈ Z ∈l ω 2 ( Z )∣u n =0 (n . When ω(n)=1 for n⩾0 and ω(n)=e|n|/log(|n|+1) for n l ω 2 ( Z ) is generated by the translates of the Fourier sequence of some singular inner function. The proofs are based on a priori estimates on the growth of the solutions of some convolution equations, obtained by using the theory of asymptotically holomorphic functions in the disc." @default.
- W2044638023 created "2016-06-24" @default.
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- W2044638023 date "2002-01-01" @default.
- W2044638023 modified "2023-09-27" @default.
- W2044638023 title "Asymptotically holomorphic functions and translation invariant subspaces of weighted Hilbert spaces of sequences" @default.
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- W2044638023 doi "https://doi.org/10.1016/s0012-9593(02)01088-1" @default.
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