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A Primer on the Dirichlet Space by Thomas Ransford, Javad Mashreghi, Karim Kellay, Omar El-Fallah

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9

Cyclicity

In the previous chapter we saw that every (closed) invariant subspace of imageμ is cyclic, in other words, that it is generated by a single function in imageμ. In this chapter, we shall take the opposite point of view: starting with fimageμ, can we identify the invariant subspace that it generates? It is easy to see that g belongs to this invariant subspace if and only if there is a sequence of polynomials (pn) such that but in practice it is often ...

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