Perturbations in Müntz's theorem

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Abstract

We generalize parts of the Müntz–Szász theorem by considering the denseness of sets span{xλ1,xλ2,}, where the λi's grow polynomially. We develop a new interpolation technique to illustrate more precisely what is missing from the closure of the Müntz sets. This is a robust technique which allows for perturbations.

MSC

primary
41A30
secondary
47A16
47B33

Keywords

Müntz's theorem
Composition operators
Cyclic vectors
Invariant subspaces

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