Complex analysis, complex variables

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Pseudoanalytic function theory generalizes and preserves many crucial features of complex analytic function theory.

This book presents and details the process of quantization of a classical mechanical system in a relevant physical system, the harmonic oscillator.

This book discusses, develops and applies the theory of Vilenkin-Fourier series connected to modern harmonic analysis.

This monograph studies decompositions of the Jacobian of a smooth projective curve, induced by the action of a finite group, into a product of abelian subvarieties.

This book describes the Hamilton-Jacobi formalism of quantum mechanics, which allowscomputation of eigenvalues of quantum mechanical potential problems without solving for thewave function.

This contributed volume showcases the most significant results obtained from the DFG Priority Program on Compressed Sensing in Information Processing.

This book surveys the foundations of the theory of slice regular functions over the quaternions, introduced in 2006, and gives an overview of its generalizations and applications.

This monograph provides a comprehensive introduction to the theory of complex normal surface singularities, with a special emphasis on connections to low-dimensional topology.

This volume presents a completely self-contained introduction to the elaborate theory of locally compact quantum groups, bringing the reader to the frontiers of present-day research.

This proceedings volume gathers selected, peer-reviewed papers presented at the 41st International Conference on Infinite Dimensional Analysis, Quantum Probability and Related Topics (QP41) that was virtually held at the United Arab Emirates University (UAEU) in Al Ain, Abu Dhabi, from March 28th to April 1st, 2021.

This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes.

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This volume includes the main contributions by the plenary speakers from the ISAAC congress held in Aveiro, Portugal, in 2019.

Deep connections exist between harmonic and applied analysis and the diverse yet connected topics of machine learning, data analysis, and imaging science.

This contributed volume provides an extensive account of research and expository papers in a broad domain of mathematical analysis and its various applications to a multitude of fields.

This book highlights a number of recent research advances in the field of symplectic and contact geometry and topology, and related areas in low-dimensional topology.

This book provides a concise survey of the theory of zero product-determined algebras, which has been developed over the last 15 years.

This book collects a series of important works on noncommutative harmonic analysis on homogeneous spaces and related topics.

This volume is part of the collaboration agreement between Springer and the ISAAC society.

This volume is part of the collaboration agreement between Springer and the ISAAC society.

This volume presents selected contributions from experts gathered at Chapman University for a conference held in November 2019 on new directions in function theory.

This monograph systematically explores the theory of rational maps between spheres in complex Euclidean spaces and its connections to other areas of mathematics.

This book investigates the close relation between quite sophisticated function spaces, the regularity of solutions of partial differential equations (PDEs) in these spaces and the link with the numerical solution of such PDEs.

This book collects the abstracts of  the mini-courses and lectures given during the Intensive Research Program "e;Spaces of Analytic Functions: Approximation, Interpolation, Sampling"e; which was held at the Centre de Recerca Matematica (Barcelona) in October-December, 2019.

This contributed volume showcases research and survey papers devoted to a broad range of topics on functional equations, ordinary differential equations, partial differential equations, stochastic differential equations, optimization theory, network games, generalized Nash equilibria, critical point theory, calculus of variations, nonlinear functional analysis, convex analysis, variational inequalities, topology, global differential geometry, curvature flows, perturbation theory, numerical analysis, mathematical finance and a variety of applications in interdisciplinary topics.

This volume originated in talks given in Cortona at the conference "e;Geometric aspects of harmonic analysis"e; held in honor of the 70th birthday of Fulvio Ricci.

This book studies solutions of the Polubarinova-Galin and Lowner-Kufarev equations, which describe the evolution of a viscous fluid (Hele-Shaw) blob, after the time when these solutions have lost their physical meaning due to loss of univalence of the mapping function involved.

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This monograph offers the first systematic treatment of the theory of minimal surfaces in Euclidean spaces by complex analytic methods, many of which have been developed in recent decades as part of the theory of Oka manifolds (the h-principle in complex analysis).

This edited volume presents state-of-the-art developments in various areas in which Harmonic Analysis is applied.

This book presents a broad overview of the important recent progress which led to the emergence of new ideas in Lipschitz geometry and singularities, and started to build bridges to several major areas of singularity theory.

This book is the second edition, whose original mission was to offer a new approach for students wishing to better understand the mathematical tenets that underlie the study of physics.

This is a brief textbook on complex analysis intended for the students of upper undergraduate or beginning graduate level.

This book originates from the session "e;Harmonic Analysis and Partial Differential Equations"e; held at the 12th ISAAC Congress in Aveiro, and provides a quick overview over recent advances in partial differential equations with a particular focus on the interplay between tools from harmonic analysis, functional inequalities and variational characterisations of solutions to particular non-linear PDEs.

This book gathers nineteen papers presented at the first NLAGA-BIRS Symposium, which was held at the Cheikh Anta Diop University in Dakar, Senegal, on June 24-28, 2019.

The present volume contains the Proceedings of the Seventh Iberoamerican Workshop in Orthogonal Polynomials and Applications (EIBPOA, which stands for Encuentros Iberoamericanos de Polinomios Ortogonales y Aplicaciones, in Spanish), held at the Universidad Carlos III de Madrid, Leganes, Spain, from July 3 to July 6, 2018.

This book provides a detailed introduction to recent developments in the theory of linear differential systems and integrable total differential systems.

This textbook explores a selection of topics in complex analysis.

This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory.

This book provides a thorough introduction to the theory of complex semisimple quantum groups, that is, Drinfeld doubles of q-deformations of compact semisimple Lie groups.

This self-contained book lays the foundations for a systematic understanding of potential theoretic and uniformization problems on fractal Sierpinski carpets, and proposes a theory based on the latest developments in the field of analysis on metric spaces.

This monograph is the first comprehensive treatment of multiplicity-free induced representations of finite groups as a generalization of finite Gelfand pairs.

This book presents English translations of Michele Sce's most important works, originally written in Italian during the period 1955-1973, on hypercomplex analysis and algebras of hypercomplex numbers.

What's the point of calculating definite integrals since you can't possibly do them all?

This book gives a systematic presentation of real algebraic varieties.

This is the revised second edition of the well-received book by the first two authors.

The contributions to this volume are devoted to a discussion of state-of-the-art research and treatment of problems of a wide spectrum of areas in complex analysis ranging from pure to applied and interdisciplinary mathematical research.