The mathematics of superoscillations / Yakir Aharonov, Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa, Jeff Tollaksen

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Memoirs of the American Mathematical Society ; volume 247, number 1174Publisher: Providence, Rhode Island : American Mathematical Society, 2017Description: 1 Online-Ressource (v, 107 pages)Subject(s): Additional physical formats: 1470423243 | 9781470423247 | 1470437090. | 9781470437091. | Erscheint auch als: No title Druck-Ausgabe | Print version: Mathematics of superoscillations DDC classification:
  • 530.12
MSC: MSC: *42A16 | 81P15 | 81Q10 | 47B38 | 35Q41LOC classification:
  • QA865
Online resources: Summary: 4.2. Convolutors on Analytically Uniform spaces4.3. Dirichlet series; Chapter 5. Schrödinger equation and superoscillations; 5.1. Schrödinger equation for the free particle; 5.2. Approximation by gaussians and persistence of superoscillations; 5.3. Quantum harmonic oscillator; Chapter 6. Superoscillating functions and convolution equations; 6.1. Convolution operators for generalized Schrödinger equations; 6.2. Formal solutions to Cauchy problems for linear constant coefficients differential equations; 6.3. Differential equations of non-Kowalevski typeSummary: Cover; Title page; Chapter 1. Introduction; Chapter 2. Physical motivations; 2.1. Overview; 2.2. Von Neumann measurements; 2.3. Weak values and weak measurements -- the main idea; 2.4. Weak values and weak measurements -- mathematical aspects; 2.5. Large weak values and superoscillations; Chapter 3. Basic mathematical properties of superoscillating sequences; 3.1. Superoscillating sequences; 3.2. Test functions and their Fourier transforms; 3.3. Approximations of functions in (ℝ); Chapter 4. Function spaces of holomorphic functions with growth; 4.1. Analytically Uniform spacesSummary: In 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 spectrumPPN: PPN: 897924762Package identifier: Produktsigel: ZDB-4-NLEBK
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