## On Landau's eigenvalue theorem and information cut-setsProfessor Massimo Franceschetti ## AbstractHow much information can be carried by electromagnetic radiation? We present a variation of a theorem of Landau concerning the phase transition of the eigenvalues of a time-frequency limiting operator, and describe its application in a limiting regime where the original theorem cannot be directly applied. Using this result, we compute the number of degrees of freedom of square-integrable fields in terms of Kolmogorovâ€™s N-width and determine, up to order, the total amount of information that can be transported in time and space by electromagnetic waves, extending previous single-frequency treatments to signals of non-zero frequency bandwidth. In closing, we also discuss how our mathematical results are related to the holographic principle of quantum gravity that has been formulated in the context of black hole thermodynamics. ## BiographyProfessor of Electrical and Computer Engineering at University of California at San Diego. Received the Laurea degree, magna cum laude, in Computer Engineering from the University of Naples in 1997, M.S. and Ph.D. degrees in Electrical Engineering from the California Institute of Technology in 1999, and 2003. Before joining UCSD, he was a post-doctoral scholar at University of California at Berkeley for two years. He was awarded: the C. H. Wilts Prize in 2003 for best doctoral thesis in Electrical Engineering at Caltech, the IEEE Transactions on Antennas and Propagation society S. A. Schelkunoff best paper award in 2005, the IEEE Communications society best tutorial paper award in 2010 the IEEE Control theory society Ruberti young researcher award in 2012. An NSF CAREER award in 2006, and an ONR Young Investigator award in 2007. He has served: as Associate Editor for of the IEEE Transactions on Information Theory (2009-2012), as as guest Associate Editor of the IEEE Journal on Selected Areas in Communication. He is currently serving: as Associate Editor of the IEEE Transactions on Control of Network Systems (2013-2016) and of the IEEE Transactions on Network Science and Engineering (2014-2017). |