Complex analysis, complex variables

The aim of this volume is two-fold.

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.

Introduction to Riemann surfaces for graduates and researchers, giving refreshingly new insights into the subject.

In two volumes, this comprehensive treatment covers all that is needed to understand and appreciate this beautiful branch of mathematics.

The monograph is concerned with the modulus of families of curves on Riemann surfaces and its applications to extremal problems for conformal, quasiconformal mappings, and the extension of the modulus onto Teichmuller spaces.

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.

This is the fifth volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research.

The great mathematician G.

This introductory text on complex variable methods has been updated with even more examples and exercises.

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 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.

A unifying approach suitable for graduate students and mathematicians.

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.

Comprehensive coverage of recent, exciting developments in Fourier restriction theory, including applications to number theory and PDEs.

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

In this monograph, for elliptic systems with block structure in the upper half-space and t-independent coefficients, the authors settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal ranges of exponents.

This book arises from the INdAM Meeting "e;Complex and Symplectic Geometry"e;, which was held in Cortona in June 2016.

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.

Complex analysis is a classic and central area of mathematics, which is studied and exploited in a range of important fields, from number theory to engineering.

Functions of bounded variation represent an important class of functions.

The real-variable theory of function spaces has always been at the core of harmonic analysis.

Despite the fundamental role played by Reshetnyak's work in the theory of surfaces of bounded integral curvature, the proofs of his results were only available in his original articles, written in Russian and often hard to find.

This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.

This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the so-called L2 $\bar{\delta}$-method.

This book contains an exposition of the theory of meromorphic functions and linear series on a compact Riemann surface.

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind.

This book gives a comprehensive introduction to those parts of the theory of elliptic integrals and elliptic functions which provide illuminating examples in complex analysis, but which are not often covered in regular university courses.

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Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry.

During his long and distinguished career, J.

Over the course of his distinguished career, Robert Strichartz (1943-2021) had a substantial impact on the field of analysis with his deep, original results in classical harmonic, functional, and spectral analysis, and in the newly developed analysis on fractals.

This book features state-of-the-art research on singularities in geometry, topology, foliations and dynamics and provides an overview of the current state of singularity theory in these settings.

An elementary account of the theory of compact Riemann surfaces and an introduction to the Belyi–Grothendieck theory of dessins d''enfants.

This volume contains contributions of principal speakers of the symposium on geometry and analysis of automorphic forms of several variables, held in September 2009 at Tokyo, Japan, in honor of Takayuki Oda's 60th birthday.

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 studies diverse aspects of braid representations via knots and links.

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During the last ten years a powerful technique for the study of partial differential equations with regular singularities has developed using the theory of hyperfunctions.

On April 25-27, 1989, over a hundred mathematicians, including eleven from abroad, gathered at the University of Illinois Conference Center at Allerton Park for a major conference on analytic number theory.

This book collects papers related to the session "e;Harmonic Analysis and Partial Differential Equations"e; held at the 13th International ISAAC Congress in Ghent and provides an overview on recent trends and advances in the interplay between harmonic analysis and partial differential equations.

This valuable collection of articles presents the latest methods and results in complex analysis and its applications.

Harmonic maps between Riemannian manifolds were first established by James Eells and Joseph H.

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