Cyclic vectors and invariant subspaces for the backward shift operator
نویسندگان
چکیده
منابع مشابه
Analytic Continuation and Embeddings in Weighted Backward Shift Invariant Subspaces
By a famous result, functions in backward shift invariant subspaces in Hardy spaces are characterized by the fact that they admit a pseudocontinuation a.e. on T. More can be said if the spectrum of the associated inner function has holes on T. Then the functions of the invariant subspaces even extend analytically through these holes. We will discuss the situation in weighted backward shift inva...
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It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as well as the functional-model space for a Hilbert space contraction operator. We discuss two multivariable extensions of this structure, where the classical H...
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Regular and irregular sampling theorems for multivariate shift invariant subspaces are studied. We give a characterization of regular points and an irregular sampling theorem, which covers many known results, e.g., Kadec’s 1/4-theorem. We show that some subspaces may not have a regular point. We also present a reconstruction algorithm which is slightly different from the known one but is more e...
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We characterize the closed operators with domain contained in the Hardy space H 2 that commute with the backward shift. Also, we give necessary and suucient conditions for such an operator to be a Toeplitz operator with symbol the complex conjugate of a function in H 2. In particular, we show that this fact depends only on the domain. Introduction. Let F be a function in the Hardy space of the ...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 1970
ISSN: 0373-0956
DOI: 10.5802/aif.338