Doubly invariant subspaces of the Besicovitch space
Sasane, A.
(2022).
Doubly invariant subspaces of the Besicovitch space.
Methods of Functional Analysis and Topology,,
28(2), 150 - 156.
https://doi.org/10.31392/MFAT-npu26_2.2022.07
(2022).
Doubly invariant subspaces of the Besicovitch space.
Methods of Functional Analysis and Topology,,
28(2), 150 - 156.
https://doi.org/10.31392/MFAT-npu26_2.2022.07
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 μ, as being the ranges of the multiplication maps corresponding to the characteristic functions of μ-measurable subsets of the unit circle. An analogue of this result is given for the Besicovitch Hilbert space of `square integrable almost periodic functions'.
