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.
Mathematics Subject Classification (2010). 32A15; 32A10; 47B38
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Colombo, F., Sabadini, I., Struppa, D.C. (2016). An Introduction to Superoscillatory Sequences. In: Alpay, D., Cipriani, F., Colombo, F., Guido, D., Sabadini, I., Sauvageot, JL. (eds) Noncommutative Analysis, Operator Theory and Applications. Operator Theory: Advances and Applications(), vol 252. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-29116-1_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-29116-1_7
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-29114-7
Online ISBN: 978-3-319-29116-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)