The Mathematical Heritage of Guido Weiss (Applied and Numerical Harmonic Analysis)

This work is a tribute to the life and work of Guido Weiss, a mathematician whose profound contributions shaped the field of harmonic analysis over a span of more than six decades. His groundbreaking research, from pioneering real and complex analysis to his later work on wavelets, continues to influence generations of scholars. More than just a researcher, Guido was a mentor, collaborator, and friend to many, creating a global community of mathematicians. His charisma and generosity fostered lasting professional and personal connections across continents, touching lives far beyond academia.

This volume features contributions of collaborators, students, and colleagues of Guido, who had a particularly intense relationship with him. From a heartfelt remembrance of Guido Weiss to advanced discussions on spectral synthesis and wavelet theory, this collection contains a diverse landscape of mathematical results.

Readers will delve into topics such as the compactness of bilinear commutators, the intricacies of analytic families in extrapolation theory, and the intersections of time-frequency analysis with modern learning techniques. With contributions to Hardy spaces, Haar multipliers, and crystalline measures, this book serves both as a tribute to past achievements and a beacon for future exploration.

Eugenio Hernández obtained his PhD from Washington University in St. Louis in 1981 under the guidance of Richard Rochberg and Guido Weiss. He has been a member of the faculty at Universidad Autónoma de Madrid, Spain, since 1982, where he is now a Professor of Mathematics. His research interests include the theory of wavelets and related systems such as frames, non-linear approximation, and invariant subspaces of unitary representations.

Marco Maria Peloso obtained his PhD from Washington University in St. Louis in 1990. He has been a Professor of Mathematical Analysis at the Università degli Studi di Milano since 2007 and was previously at the Politecnico di Torino. He has held visiting positions at Michigan State University, the University of Missouri - Columbia, Washington University in St. Louis, and the University of Arkansas - Fayetteville. His research interests are in harmonic analysis, complex analysis in one and several variables, and related areas.

Fulvio Ricci obtained his PhD from the University of Maryland in 1977 under the guidance of John Benedetto. He has been a Professor of Mathematical Analysis in Italy, first at the Politecnico di Torino and, since 2000, at the Scuola Normale Superiore di Pisa, where he is now Professor Emeritus. His research interests focus on harmonic analysis in Euclidean spaces and Lie groups.

Fernando Soria obtained his PhD under the supervision of Mitchell Taibleson and Guido Weiss at Washington University in St. Louis. His mathematical interests have followed those of Guido Weiss over the years, encompassing harmonic analysis, singular integrals, and wavelets. More recently, he has been working in the area of nonlocal partial differential equations. He has been a Professor of Mathematics at Universidad Autónoma de Madrid since 1992.

Anita Tabacco obtained her PhD from Washington University in St. Louis in 1986 under the guidance of Richard Rochberg and Guido Weiss. She has been a Professor of Mathematical Analysis at the Department of Mathematical Sciences at the Politecnico di Torino, Italy, since 1992. Her research interests include real and complex analysis, functional analysis, and harmonic analysis. She is also involved in the field of engineering education and university management.