Complex analysis, complex variables

The purpose of this book is to develop the foundations of the theory of holomorphicity on the ring of bicomplex numbers.

This volume provides an introduction to dessins d'enfants and embeddings of bipartite graphs in compact Riemann surfaces.

This book provides an introduction to the basic ideas and tools used in mathematical analysis.

This book contains a history of real and complex analysis in the nineteenth century, from the work of Lagrange and Fourier to the origins of set theory and the modern foundations of analysis.

The purpose of this book is to provide an overview of historical and recent results on concentration inequalities for sums of independent random variables and for martingales.

This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints.

The monograph is devoted to integral representations for holomorphic functions in several complex variables, such as Bochner-Martinelli, Cauchy-Fantappie, Koppelman, multidimensional logarithmic residue etc.

This book focuses on complex geometry and covers highly active topics centered around geometric problems in several complex variables and complex dynamics, written by some of the world's leading experts in their respective fields.

This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 - 2013.

Reconstructing or approximating objects from seemingly incomplete information is a frequent challenge in mathematics, science, and engineering.

This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing.

Extending Griffiths' classical theory of period mappings for compact Kahler manifolds, this book develops and applies a theory of period mappings of "e;Hodge-de Rham type"e; for families of open complex manifolds.

This introductory graduate level text provides a relatively quick path to a special topic in classical differential geometry: principal bundles.

This book gathers peer-reviewed contributions representing modern trends in the theory of generalized functions and pseudo-differential operators.

This book takes an in-depth look at abelian relations of codimension one webs in the complex analytic setting.

This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 - 2013.

This book is a collection of papers from the 9th International ISAAC Congress held in 2013 in Krakow, Poland.

The international workshop on which this proceedings volume is based on brought together leading researchers in the field of elliptic and parabolic equations.

This monograph grew out of the authors' efforts to provide a natural geometric description for the class of maps invariant under parabolic renormalization and for the Inou-Shishikura fixed point itself as well as to carry out a computer-assisted study of the parabolic renormalization operator.

This volume is dedicated to the memory of Shoshichi Kobayashi, and gathers contributions from distinguished researchers working on topics close to his research areas.

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This is a monograph devoted to recent research and results on dynamic inequalities on time scales.

We introduce mixed twistor D-modules and establish their fundamental functorial properties.

Gathering and updating results scattered in journal articles over thirty years, this self-contained monograph gives a comprehensive introduction to the subject.

Hypercomplex analysis is the extension of complex analysis to higher dimensions where the concept of a holomorphic function is substituted by the concept of a monogenic function.

This monograph covers a multitude of concepts, results, and research topics originating from a classical moving-boundary problem in two dimensions (idealized Hele-Shaw flows, or classical Laplacian growth), which has strong connections to many exciting modern developments in mathematics and theoretical physics.

Probability theory on compact Lie groups deals with the interaction between "e;chance"e; and "e;symmetry,"e; a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing).

This volume presents significant advances in a number of theories and problems of Mathematical Analysis and its applications in disciplines such as Analytic Inequalities, Operator Theory, Functional Analysis, Approximation Theory, Functional Equations, Differential Equations, Wavelets, Discrete Mathematics and Mechanics.

The purpose of this book is to provide an integrated course in real and complex analysis for those who have already taken a preliminary course in real analysis.

This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula.

This book provides the foundations for a rigorous theory of functional analysis with bicomplex scalars.

The main purpose of this book is to provide a simple and accessible introduction to the mixed finite element method as a fundamental tool to numerically solve a wide class of boundary value problems arising in physics and engineering sciences.

In this book we introduce the class of mappings of finite distortion as a generalization of the class of mappings of bounded distortion.

This book provides a survey on wide-spread of employing wavelets analysis in different applications of speech processing.

This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis.

In these notes, we provide a summary of recent results on the cohomological properties of compact complex manifolds not endowed with a Kahler structure.

This volume highlights the main results of the research performed within the network "e;Harmonic and Complex Analysis and its Applications"e; (HCAA), which was a five-year (2007-2012) European Science Foundation Programme intended to explore and to strengthen the bridge between two scientific communities: analysts with broad backgrounds in complex and harmonic analysis and mathematical physics, and specialists in physics and applied sciences.

This book presents a comprehensive introduction to the concepts of almost periodicity, asymptotic almost periodicity, almost automorphy, asymptotic almost automorphy, pseudo-almost periodicity, and pseudo-almost automorphy as well as their recent generalizations.

This volume collects lecture notes from courses offered at several conferences and workshops, and provides the first exposition in book form of the basic theory of the Kahler-Ricci flow and its current state-of-the-art.

This book studies some of the groundbreaking advances that have been made regarding analytic capacity and its relationship to rectifiability in the decade 1995-2005.

The theory of complex functions is a strikingly beautiful and powerful area of mathematics.

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

This textbook explores a selection of topics in complex analysis.

This book is the second of a two volume series.

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.