Doubly invariant subspaces of the Besicovitch space

2021/05/11 by Amol Sasane, Sasane, Amol
Mathematics · #43A75 #47B38 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA) #Primary 42A75 #Secondary 47A15

paper · pdf · doi:10.48550/arxiv.2105.05215

openalex publication_date 2021/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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'.

Related

• A Besicovitch-Morse function preserving the Lebesgue measure
• A Beurling Theorem for almost-invariant subspaces of the shift operator
• Constructions of some families of smooth Cauchy transforms
• Bohr's equivalence relation in the space of Besicovitch almost periodic functions
• Nearly invariant subspaces for operators in Hilbert spaces