The ‘window problem’ for series of complex exponentials

By T. Seidman, S. Avdonin, S. Ivanov. 2000

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Observation and Control for Operator Semigroups (2009, result): “We refer to Seidman [206], Seidman, Avdonin and Ivanov [207], Miller [170] and Tenenbaum and Tucsnak [218] for results in this direction.”
On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials (2008, background): “We refer also to [23] for a discussion of the optimal growth rate in one space dimension.”
Controllability and Observability of Partial Differential Equations: Some Results and Open Problems (2007, background): “We refer also to [176] for a discussion of the optimal growth rate in one space dimension.”
New blow-up rates for fast controls of Schrödinger and heat equations (2007, background): “1), this result improves the constants obtained in [22]—see [14] for detailed comments on this issue.”
A complex-analytic approach to the problem of uniform controllability of a transport equation in the vanishing viscosity limit (2010, methodology): “By a completely different method, relying on complex analysis, we prove that this still holds when T > 4.2 L/M if M > 0 and when T > 6.1 L/|M | if M < 0.”
On the lack of null-controllability of the heat equation on the half-line (2000, unknown): “In Section 3 we define the solutions, derive the corresponding moment problem, and state and prove the main results.”