Introduction to Superoscillations: Past and Present

Yakir Aharonov (), Fabrizio Colombo (), Irene Sabadini () and Daniele C. Struppa ()
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Yakir Aharonov: Chapman University, James J. Farley Professorship in Natural Philosophy Director of the Institute for Quantum Studies
Fabrizio Colombo: Politecnico di Milano, Dipartimento di Matematica
Irene Sabadini: Politecnico di Milano, Dipartimento di Matematica
Daniele C. Struppa: Chapman University, The Kennedy Chair in Mathematics

Chapter 91 in Operator Theory, 2026, pp 2809-2834 from Springer

Abstract: Abstract The aim of this chapter is to provide readers with an overview of the recent developments in the theory of superoscillations and supershifts. The concept of superoscillations dates back many years, with numerous contributions from various authors. However, it is within the last 15 years that the theory of superoscillatory functions and the related concept of supershifts have emerged as a significant area within mathematics. In this chapter, we explore the early development and the most recent advancements in this field, and we provide an updated list of references that accurately illustrate the state of the art.

Keywords: Superoscillating functions; Supershifts; Convolution operators; Schrödinger equation; Entire functions with growth conditions; 32A15; 32A10; 47B38 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16356-1_96

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