Advertisement

An Introduction to Superoscillatory Sequences

  • Fabrizio ColomboEmail author
  • Irene Sabadini
  • Daniele C. Struppa
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 252)

Abstract

The notion of superoscillating functions, or more properly of superoscillatory sequences, is a byproduct of Aharonov’s theory of weak measurements and weak values in quantum mechanics. Recently, many mathematicians and physicists have begun to pay attention to the mathematical significance of such objects, and have been able to begin a theory of superoscillatory behavior. Not surprisingly, this theory is based on some classical results in Fourier analysis, and it displays interesting connections with the theory of convolution equations. In this paper we will put these connections in a larger context, and show how to use this context to generate a large class of superoscillating sequences. As a concrete example we discuss the Cauchy problem with superoscillatory datum for the harmonic oscillator. Finally, we show how this theory can be generalized to the case of several variables.

Keywords

Superoscillating sequences spaces of holomorphic functions series of differential operators 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Fabrizio Colombo
    • 1
    Email author
  • Irene Sabadini
    • 1
  • Daniele C. Struppa
    • 2
  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  2. 2.Schmid College of Science and TechnologyChapman University, One University driveOrangeUSA

Personalised recommendations