Lectures on invariant subspaces

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The Structure of Translation-Invariant Spaces on Locally Compact Abelian Groups (2015, unknown): “We characterize such spaces in terms of range functions which originated in the characterization of doubly invariant spaces by Helson [17] and Srinivasan [32].”
Subspaces of L2(G) invariant under translation by an abelian subgroup (2014, unknown): “We say that J is a measurable range function if, for each (u, v) ∈ H × H, the function x 7→ 〈PJ(x)u, v〉 is measurable on X. Range functions have a long history in the classification of invariant subspaces, dating at least as far back as Helson [19] and Srinivasan [36] in 1964.”
Linear Stochastic Systems: A Geometric Approach to Modeling, Estimation and Identification (2016, methodology): “Starting with [44, 91], generalizations of “Wold Decomposition” theory have become part of functional analysis and have led to a unifying view of certain fundamental problems in operator theory and Hardy spaces [46].”
Inner functions on the bidisk and associated Hilbert spaces (2012, background): “See [18] or [28] for the one variable theory.”
The Zak transform and the structure of spaces invariant by the action of an LCA group (2014, background): “In the setting of Helson [20, 21], a determining set is the set of exponentials with integer parameter, D = {e2πik·}k∈Z ⊆ L∞(T).”