Published by De Gruyter

Advances in Analysis and Geometry

Edited by: Jie Xiao

ISSN: 2511-0438

e-ISSN 2511-0543

Overview
Volumes

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 Board
Der-Chen Chang, Georgetown University, USA
Goong Chen, Texas A&M University, USA
Andrea Colesanti, University of Florence, Italy
Robert 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.

Book 2023

Harmonic Analysis and Convexity

Alexander Koldobsky, Alexander Volberg

Volume 9 in this series

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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.

DOI:: https://doi.org/10.1515/9783110775389
ISBN:: 9783110775389
ISBN:: 9783110775433
ISBN:: 9783110775372
Subject:: Mathematics
Subject:: Analysis
Subject:: Geometry and Topology
Subject:: Probability and Statistics
Subject:: Physics
Subject:: Theoretical and Mathematical Physics
Publisher:: De Gruyter

Book 2023

Potentials and Partial Differential Equations

The Legacy of David R. Adams

Suzanne Lenhart, Jie Xiao

Volume 8 in this series

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This volume is dedicated to the legacy of David R. Adams (1941-2021) and discusses calculus of variations, functional - harmonic - potential analysis, partial differential equations, and their applications in modeling, mathematical physics, and differential - integral geometry.

DOI:: https://doi.org/10.1515/9783110792720
ISBN:: 9783110792720
ISBN:: 9783110792782
ISBN:: 9783110792652
Subject:: Mathematics
Subject:: Analysis
Subject:: Differential Equations and Dynamical Systems
Subject:: Applied Mathematics
Publisher:: De Gruyter

Book 2022

The Sub-Laplacian Operators of Some Model Domains

Der-Chen Chang, Jingzhi Tie

Volume 7 in this series

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The book constructs explicitly the fundamental solution of the sub-Laplacian operator for a family of model domains in Cn+1. This type of domain is a good point-wise model for a Cauchy-Rieman (CR) manifold with diagonalizable Levi form. Qualitative results for such operators have been studied extensively, but exact formulas are difficult to derive. Exact formulas are closely related to the underlying geometry and lead to equations of classical types such as hypergeometric equations and Whittaker’s equations.

DOI:: https://doi.org/10.1515/9783110642995
ISBN:: 9783110642995
ISBN:: 9783110642100
ISBN:: 9783110643176
Subject:: Mathematics
Subject:: Analysis
Publisher:: De Gruyter

Book 2022

Geometric Potential Analysis

Mario Milman, Jie Xiao, Boguslaw Zegarlinski

Volume 6 in this series

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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.

DOI:: https://doi.org/10.1515/9783110741711
ISBN:: 9783110741711
ISBN:: 9783110741896
ISBN:: 9783110741674
Subject:: Mathematics
Subject:: Analysis
Subject:: Differential Equations and Dynamical Systems
Subject:: Geometry and Topology
Subject:: Physics
Subject:: Theoretical and Mathematical Physics
Publisher:: De Gruyter

Book 2022

Real Hypersurfaces in Hermitian Symmetric Spaces

Jürgen Berndt, Young Jin Suh

Volume 5 in this series

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Hermitian symmetric spaces are an important class of manifolds that can be studied with methods from Kähler geometry and Lie theory. This work gives an introduction to Hermitian symmetric spaces and their submanifolds, and presents classifi cation results for real hypersurfaces in these spaces, focusing on results obtained by Jürgen Berndt and Young Jin Suh in the last 20 years.

DOI:: https://doi.org/10.1515/9783110689839
ISBN:: 9783110689839
ISBN:: 9783110689914
ISBN:: 9783110689785
Subject:: Mathematics
Subject:: Geometry and Topology
Publisher:: De Gruyter

Book 2021

Quantum Harmonic Analysis

An Introduction

Maurice A. de Gosson

Volume 4 in this series

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Quantum mechanics is arguably one of the most successful scientific theories ever and its applications to chemistry, optics, and information theory are innumerable. This book provides the reader with a rigorous treatment of the main mathematical tools from harmonic analysis which play an essential role in the modern formulation of quantum mechanics. This allows us at the same time to suggest some new ideas and methods, with a special focus on topics such as the Wigner phase space formalism and its applications to the theory of the density operator and its entanglement properties. This book can be used with profit by advanced undergraduate students in mathematics and physics, as well as by confirmed researchers.

DOI:: https://doi.org/10.1515/9783110722772
ISBN:: 9783110722772
ISBN:: 9783110722611
ISBN:: 9783110722901
Subject:: Mathematics
Subject:: Analysis
Subject:: Probability and Statistics
Subject:: Physics
Subject:: Theoretical and Mathematical Physics
Publisher:: De Gruyter

Book 2021

Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs

Alexander Grigor'yan, Yuhua Sun

Volume 3 in this series

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The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.

DOI:: https://doi.org/10.1515/9783110700763
ISBN:: 9783110700763
ISBN:: 9783110700633
ISBN:: 9783110700855
Subject:: Mathematics
Subject:: Analysis
Subject:: Differential Equations and Dynamical Systems
Publisher:: De Gruyter

Book 2020

The Mathematical Legacy of Victor Lomonosov

Operator Theory

Richard M. Aron, Eva A. Gallardo Gutiérrez, Miguel Martin, Dmitry Ryabogin, Ilya M. Spitkovsky, Artem Zvavitch

Volume 2 in this series

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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.

DOI:: https://doi.org/10.1515/9783110656756
ISBN:: 9783110656756
ISBN:: 9783110653397
ISBN:: 9783110653465
Subject:: Mathematics
Subject:: Analysis
Publisher:: De Gruyter

Book 2019

Qα Analysis on Euclidean Spaces

Jie Xiao

Volume 1 in this series

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Starting with the fundamentals of Qα spaces and their relationships to Besov spaces, this book presents all major results around Qα spaces obtained in the past 16 years. The applications of Qα spaces in the study of the incompressible Navier-Stokes system and its stationary form are also discussed. This self-contained book can be used as an essential reference for researchers and graduates in analysis and partial differential equations.

DOI:: https://doi.org/10.1515/9783110600285
ISBN:: 9783110600285
ISBN:: 9783110601121
ISBN:: 9783110600100
Subject:: Mathematics
Subject:: Analysis
Subject:: Differential Equations and Dynamical Systems
Publisher:: De Gruyter