Iker Gardeazabal will defend his thesis on Friday, October 31st

The defence will take place at Sala Adela Moyua Faculty of Science and Technology (EHU - Leioa) at 11:00

Iker Gardeazabal Gutiérrez has been a PhD student at BCAM since August 2021, in the Harmonica Analysis group. Previously, he obtained his Bachelor's degree in Mathematics from the University of the Basque Country in 2019 and the Master's degree in Advanced Mathematics from the Complutense University of Madrid in 2020. His research focuses on two main topics, each developed with one of his supervisors: the first, generalized Poincaré inequalities, with Cralos Pérez Moreno, and the second, interpolation formulas for band limited functions, with Mateus Sousa.

His thesis, titled “Generalized Poincaré inequalities and interpolation formulas for band limited functions" is supervised by Prof. Carlos Pérez (BCAM & UPV/EHU) and Mateus Costa (BCAM). It is scheduled to be defended on October 31st, 2025, at Sala Adela Moyua, Faculty of Science and Technology (EHU - Leioa) at 11:00 a.m. 

On behalf of all members of BCAM, we would like to wish him all the best for the future, both professionally and personally.

Abstract

This thesis focuses on two main topics, generalized Poincaré inequalities and interpolation formulas for bandlimited functions. Regarding the first topic we generalize previously existing self-improving results for this kind of inequalities, considering cases with general doubling measures and the ones generally associated with higher order derivatives. We then use these results to obtain various inequalities mostly related to Poincaré-Sobolev inequalities as well as other new applications, such as Gagliardo-Nirenberg interpolation type inequalities. For the second topic, we develop a method to obtain interpolation formulas in the Paley–Wiener spaces, spaces of L2 functions with compactly supported Fourier transform. Specifically, we consider formulas depending on the data Tn(f)(N m), where m is any integer number, n ranges between 1 and N, N is a natural number, and Tn are Fourier multiplier operators. We obtain a necessary and sufficient condition on these operators for the interpolation formula to exist.