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arXiv · 2105.05215

Doubly invariant subspaces of the Besicovitch space

Amol Sasane
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Abstract

A classical result of Norbert Wiener characterises doubly shift-invariant subspaces for square integrable functions on the unit circle with respect to a finite positive Borel measure $\mu$, as being the ranges of the multiplication maps corresponding to the characteristic functions of $\mu$-measurable subsets of the unit circle. An analogue of this result is given for the Besicovitch Hilbert space of `square integrable almost periodic functions'.

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Amol Sasane. 2021-05-11. Doubly invariant subspaces of the Besicovitch space. https://arxiv.org/abs/2105.05215

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