# An Introduction to Superoscillatory Sequences

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## Description

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.

## ISBN

978-3-319-29116-1

## Publication Date

2016

## Publisher

Springer

## Keywords

superoscillating sequences, spaces of holomorphic functions, series of differential operators

## Disciplines

Algebraic Geometry | Other Mathematics | Quantum Physics

## Recommended Citation

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, J.-L. (Eds.), Noncommutative Analysis, Operator Theory and Applications, Operator Theory: Advances and Applications. Switzerland: Springer International Publishing, pp. 105–121.

## Copyright

Springer

## Comments

In Daniel Alpay, Fabio Cipriani, Fabrizio Colombo, Daniele Guido, Irene Sabadini, Jean-Luc Sauvageot (Eds.),

. Dr. Struppa's and Dr. Tollaksen's chapter begins on page 105.Noncommutative Analysis, Operator Theory and Applications, Operator Theory: Advances and ApplicationsThis text is only partially available through the link provided; some pages are not included. Please visit your local library or purchase the book through the "Buy This Book" link above to read the full text.