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Explore complex analysis, thick sets, and spectral inequalities in this seminar talk from the Spectral Geometry in the Clouds series. Delve into the connection between null-controllability in control theory and final-state-observability of dual systems. Examine the crucial role of spectral inequalities in demonstrating these properties. Learn about a general framework based on complex analytical techniques for obtaining spectral inequalities across various domains, operators, and graphs. Discover how these concepts extend Kovrijkine's methods for studying functions with compactly supported Fourier Transforms. Gain insights from the collaborative work of Michela Egidi, Ivan Veselic, Albrecht Seelmann, and Delio Mugnolo as they present their findings in this hour-long presentation from the Centre de recherches mathématiques.
