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OverviewIn the past 50 years, quantum physicists have discovered, and experimentally demonstrated, a phenomenon which they termed superoscillations. Aharonov and his collaborators showed that superoscillations naturally arise when dealing with weak values, a notion that provides a fundamentally different way to regard measurements in quantum physics. From a mathematical point of view, superoscillating functions are a superposition of small Fourier components with a bounded Fourier spectrum, which result, when appropriately summed, in a shift that can be arbitrarily large, and well outside the spectrum. The purpose of this work is twofold: on one hand the authors provide a self-contained survey of the existing literature, in order to offer a systematic mathematical approach to superoscillations; on the other hand, they obtain some new and unexpected results, by showing that superoscillating sequences can be seen of as solutions to a large class of convolution equations and can therefore be treated within the theory of analytically uniform spaces. In particular, the authors will also discuss the persistence of the superoscillatory behavior when superoscillating sequences are taken as initial values of the Schrodinger equation and other equations. Full Product DetailsAuthor: Y. Aharonov , F. Colombo , I. Sabadini , D.C. StruppaPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.180kg ISBN: 9781470423247ISBN 10: 1470423243 Pages: 107 Publication Date: 30 May 2017 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsIntroduction Physical motivations Basic mathematical properties of superoscillating sequences Function spaces of holomorphic functions with growth Schrodinger equation and superoscillations Superoscillating functions and convolution equations Superoscillating functions and operators Superoscillations in $SO(3)$ Bibliography IndexReviewsAuthor InformationF. Colombo, Politecnico di Milano, Italy. I. Sabadini, Polytechnic Institute of Milan, Italy. D. C. Struppa, Chapman University, Orange, CA. J. Tollaksen, Chapman University, Orange, CA. Y. Aharonov, Chapman University, Orange, CA. Tab Content 6Author Website:Countries AvailableAll regions |