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Full-Text Articles in Physical Sciences and Mathematics
Nonlinear Potential Analysis On Sobolev Multiplier Spaces, Keng Hao Ooi
Nonlinear Potential Analysis On Sobolev Multiplier Spaces, Keng Hao Ooi
LSU Doctoral Dissertations
We characterize preduals and Kothe duals to a class of Sobolev multiplier type spaces. Our results fit in well with the modern theory of function spaces of harmonic analysis and are also applicable to nonlinear partial differential equations. As a maneuver, we make use of several tools from nonlinear potential theory, weighted norm inequalities, and the theory of Banach function spaces to obtain our results. After characterizing the preduals, we establish a capacitary strong type inequality which resolves a special case of a conjecture by David R. Adams. As a consequence, we obtain several equivalent norms for Choquet integrals associated …
Entropic Bounds On Two-Way Assisted Secret-Key Agreement Capacities Of Quantum Channels, Noah Anthony Davis
Entropic Bounds On Two-Way Assisted Secret-Key Agreement Capacities Of Quantum Channels, Noah Anthony Davis
LSU Doctoral Dissertations
In order to efficiently put quantum technologies into action, we must know the characteristics of the underlying quantum systems and effects. An interesting example is the use of the secret-key-agreement capacity of a quantum channel as a guide and measure for the implementation of quantum key distribution (QKD) and distributed quantum computation. We define the communication task of establishing a secret key over a quantum channel subject to an energy constraint on the input state and while allowing for unlimited local operations and classical communication (LOCC) between a sender and receiver. We then use the energy-constrained squashed entanglement to bound …