Meromorphic Inner Functions, Toeplitz Kernels and the Uncertainty Principle

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Recent Progress on Truncated Toeplitz Operators (2011, background): “These spaces were first considered and characterized in [68, 87] and they continue to be the focus of intense study [8, 9, 22, 66, 73, 76].”
Uniqueness (2021, unknown): “Probably the best known uniqueness result in the calculus of variations is the following: If I is a strictly convex functional, deﬁned on an open convex subset of a normed space, then it has at most one critical point, which is the global minimum whenever it exists.”
Beurling-Malliavin theory for Toeplitz kernels (2007, methodology): “To make the proof self-contained, in several places we had to repeat the argument outlined in [24].”
Polya sequences, Toeplitz kernels and gap theorems (2009, methodology): “Remark. As noted in [ 15 ], the part (i) of Theorem III holds without the assumption 0(t) > const:”
Completeness and spectral synthesis of nonselfadjoint one-dimensional perturbations of selfadjoint operators (2012, background): “nential type. Finally, we remark that applications of de Branges spaces to the spectral theory of discrete selfadjoint operators and their perturbations are numerous and well-known, see for instance, [52] and also papers [58] and [75], that are closely related to our approach. 3. Positive results on”