Bøger i Advances in Analysis and Geometry serien

The series is devoted to the publication of high-level monographs and specialized graduate texts which cover classical and modern analysis, partial differential equations with natural connections to geometry and the interplays between these fields and their applications to mathematical physics. Editor-in-Chief Jie Xiao, Memorial University, Canada Editorial BoardDer-Chen Chang, Georgetown University, USA Goong Chen, Texas A&M University, USA Andrea Colesanti, University of Florence, ItalyRobert McCann, University of Toronto, Canada De-Qi Zhang, National University of Singapore, Singapore Kehe Zhu, University at Albany, USA Please send any book proposals to Jie Xiao.

The fundamental contributions made by the late Victor Lomonosov in several areas of analysis are revisited in this book, in particular, by presenting new results and future directions from world-recognized specialists in the field. The invariant subspace problem, Burnside¿s theorem, and the Bishop-Phelps theorem are discussed in detail. This volume is an essential reference to both researchers and graduate students in mathematical analysis.

This monograph contains papers that were delivered at the special session on Geometric Potential Analysis, that was part of the Mathematical Congress of the Americas 2021, virtually held in Buenos Aires. The papers, that were contributed by renowned specialists worldwide, cover important aspects of current research in geometrical potential analysis and its applications to partial differential equations and mathematical physics.

In recent years, the interaction between harmonic analysis and convex geometry has increased which has resulted in solutions to several long-standing problems. This collection is based on the topics discussed during the Research Semester on Harmonic Analysis and Convexity at the Institute for Computational and Experimental Research in Mathematics in Providence RI in Fall 2022. The volume brings together experts working in related fields to report on the status of major problems in the area including the isomorphic Busemann-Petty and slicing problems for arbitrary measures, extremal problems for Fourier extension and extremal problems for classical singular integrals of martingale type, among others.