Complex analysis, complex variables

This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research.

This volume is an outcome of the workshop "e;Moduli of K-stable Varieties"e;, which was held in Rome, Italy in 2017.

Different aspects of harmonic analysis, complex analysis, sampling theory, approximation theory and related topics are covered in this volume.

This book explains the foundations of holomorphic curve theory in contact geometry.

The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H.

This book presents the extensions to the quaternionic setting of some of the main approximation results in complex analysis.

Authored by a ranking authority in Gaussian harmonic analysis, this book embodies a state-of-the-art entree at the intersection of two important fields of research: harmonic analysis and  probability.

The chapters in this volume are based on talks given at the inaugural Aspects of Time-Frequency Analysis conference held in Turin, Italy from July 5-7, 2017, which brought together experts in harmonic analysis and its applications.

This book describes recent developments as well as some classical results regarding holomorphic mappings.

This book is a collection of short papers from the 11th International ISAAC Congress 2017 in Vaxjo, Sweden.

Functions of bounded variation represent an important class of functions.

This book offers a unified presentation of Fourier theory and corresponding algorithms emerging from new developments in function approximation using Fourier methods.

This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves.

This is a book comprising selected papers of colleagues and friends of Heinrich Begehr on the occasion of his 80th birthday.

This book focuses on a conjectural class of zeta integrals which arose from a program born in the work of Braverman and Kazhdan around the year 2000, the eventual goal being to prove the analytic continuation and functional equation of automorphic L-functions.

This book develops a spectral theory for the integrable system of 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation.

This book, intended to commemorate the work of Paul Dirac, highlights new developments in the main directions of Clifford analysis.

This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves.

New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods.

This book reviews research on single-electron devices and circuits in silicon.

The principle of local activity explains the emergence of complex patterns in a homogeneous medium.

Uncertainty is an inseparable component of almost every measurement and occurrence when dealing with real-world problems.

The subject of fractional calculus has gained considerable popularity and importance during the past three decades, mainly due to its validated applications in various fields of science and engineering.

This book introduces complex analysis and is appropriate for a first course in the subject at typically the third-year University level.

A problem factory consists of a traditional mathematical analysis of a type of problem that describes many, ideally all, ways that the problems of that type can be cast in a fashion that allows teachers or parents to generate problems for enrichment exercises, tests, and classwork.

Mathematics of Networks: Modulus Theory and Convex Optimization explores the question: "e;What can be learned by adapting the theory of p-modulus (and related continuum analysis concepts) to discrete graphs?

Mathematics of Networks: Modulus Theory and Convex Optimization explores the question: "e;What can be learned by adapting the theory of p-modulus (and related continuum analysis concepts) to discrete graphs?

This book is dedicated to the first ten years of Chaos and Complexity Letters - International Journal of Dynamical Systems Research.

Several scientists learn only a first course in complex analysis, and hence they are not familiar with several important properties: every polygenic function defines a congruence of clocks; the basic properties of algebraic functions and abelian integrals; how mankind arrived at a rigorous definition of Riemann surfaces; the concepts of dianalytic structures and Klein surfaces; the Weierstrass elliptic functions; the automorphic functions discovered by Poincare' and their links with the theory of Fuchsian groups; the geometric structure of fractional linear transformations; Kleinian groups; the Heisenberg group and geometry of the complex ball; complex powers of elliptic operators and the theory of spectral zeta-functions; an assessment of the Poincare' and Dieudonne' definitions of the concept of asymptotic expansion.

The purpose of this book is to present the classical analytic function theory of several variables as a standard subject in a course of mathematics after learning the elementary materials (sets, general topology, algebra, one complex variable).

This text is an introduction to harmonic analysis on symmetric spaces, focusing on advanced topics such as higher rank spaces, positive definite matrix space and generalizations.

This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi-Yau varieties and string theory.

Nolan Wallach's mathematical research is remarkable in both its breadth and depth.

The purpose of the corona workshop was to consider the corona problem in both one and several complex variables, both in the context of function theory and harmonic analysis as well as the context of operator theory and functional analysis.

This text is aimed at graduate students in mathematics and to interested researchers who wish to acquire an in depth understanding of Euclidean Harmonic analysis.

The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces.

This volume contains the first two out of four chapters which are intended to survey a large part of the theory of theta functions.

The theory of functional equations has been developed in a rapid and productive way in the second half of the Twentieth Century.

1.

In many situations in approximation theory the distribution of points in a given set is of interest.

For a given meromorphic function I(z) and an arbitrary value a, Nevanlinna's value distribution theory, which can be derived from the well known Poisson-Jensen for- mula, deals with relationships between the growth of the function and quantitative estimations of the roots of the equation: 1 (z) - a = O.

Analytic Extension is a mysteriously beautiful property of analytic functions.

This volume consists of papers presented in the special sessions on "e;Wave Phenomena and Related Topics"e;, and "e;Asymptotics and Homogenization"e; of the ISAAC'97 Congress held at the University of Delaware, during June 2-7, 1997.