Keywords

• superoscillation
• super-shift
• analyticity

Abstract The phenomenon of superoscillations has been generalized and has given rise to the concept of super-shift. With this terminology one usually refers to functions that, if known on a countable number of points near the origin, are completely determined throughout the real line. This concept, in a way, seems to be a form of analyticity, if the countable number of points are collapsed to be the infinite derivatives in the origin.

In this talk I will report on some joint work with Fabrizio Colombo, Irene Sabadini, and Alain Yger, and I will discuss the complex connections between these two concepts.