José Luis Romero

Best Paper Award 2018

José Luis Romero wird für sein Paper Sampling theorems for shift-invariant spaces, Gabor frames, and totally positive functions, publiziert in „Inventiones mathematicae”, March 2018, Volume 211, Issue 3, pp 1119–1148, ausgezeichnet, das er gemeinsam mit Karlheinz Gröchenig (Institut für Mathematik der Universität Wien) und Joachim Stöckler (Institut für Angewandte Mathematik der TU Dortmund) verfasst hat.

Sampling theory aims to answer the question of data digitalization: how can representative values of an analog signal be chosen, so that its fundamental characteristics are preserved? Shannon's sampling theory provides a conclusive answer: the rate at which a signal is acquired or sampled must be inversely proportional to the amount of variability or oscillation present in the signal.

Such precise mathematical answers, valid under idealized conditions, are widely used in the modern engineering literature, beyond their formal scope, as heuristic support for more realistic sampling practices. This results in a gap between theory and practice, which our work addresses by providing a complete geometric description of sampling schemes in certain practically relevant settings. The main contribution is in developing mathematical tools that are applicable to non-idealized scenarios, and yet retain the full sharpness of the classical ones.

The applications include Gabor expansions, which are signal representations in terms of short-range oscillatory patterns, and are instrumental in numerical analysis, acoustics, quantum mechanics, audio processing and wireless communications. Our analysis has bridged certain discrepancies between experimental performance and theoretical guarantees in that field.

Der Preisträger

José Luis Romero habilitierte sich 2016 im Fach Mathematik an der Universität Wien; er ist Assistent an der Universität Wien und wissenschaftlicher Mitarbeiter am Institut für Schallforschung der ÖAW. José Luis Romero schloss 2011 das Doktoratsstudium Mathematik an der Universität Buenos Aires ab. Nach einem Fulbright Stipendium an der Universität Maryland erhielt er eine Postdoc-Stelle an der Fakultät für Mathematik der Universität Wien (2011-2013); er war von 2013-2014 Lise-Meitner-Stipendiat des FWF und von 2014-2016 Marie-Skłodowska-Curie-Stipendiat der Europäischen Kommission.