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Growth of Sobolev norms for abstract linear Schrödinger equations

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No logo availableBanff International Research Station (BIRS) for Mathematical Innovation and Discovery
 Maspero, Alberto

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Growth of Sobolev norms for abstract linear Schrödinger equations
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Growth of Sobolev norms in linear time dependent Schrödinger equations
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22
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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In the talk I will present some recent results on upper and lower bounds for the growth of Sobolev norms in linear time dependent Schrödinger equations. After discussing the known upper bounds on the Sobolev norms of the solutions, I will explain a strategy to construct time dependent perturbations which provoke transfer of energy from low to high modes, leading to unbounded solutions.