University of Heidelberg, **Applied Analysis Seminar**

Dr. Joao Pedro Ramos (IMPA, Brazil)

Perturbed interpolation formulae and applications

*Online via HeiCONF*

Perturbed interpolation formulae and applications

The Radchenko-Viazovska interpolation formula tells us that we can recover the values of an even, real-valued Schwartz function $f$ from its values and the values of its Fourier transform at $sqrt{n},$ where $n \geq 0$ is an integer. This result can be seen, for instance, as a more symmetric version of the Shannon--Whittaker interpolation formula for band-limited functions, where one extracts an 'equal' amount of information from function and Fourier transform.

In this talk, we will discuss problems around this interpolation formula and generalizations. In particular, we will prove interpolation formulae with similar asymptotic distribution to that of Radchenko and Viazovska, but with perturbed interpolation nodes. As consequences of our results and methods, we will derive consequences such as the existence of exotic examples of crystalline measures, as well as new interpolation formulae with perturbed nodes with information on the derivative level. This is based off joint work with M. Sousa.

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