Complex analysis, complex variables

Thurston maps are topological generalizations of postcritically-finite rational maps.

Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects.

I - Entire functions of several complex variables constitute an important and original chapter in complex analysis.

The theory of General Relativity, after its invention by Albert Einstein, remained for many years a monument of mathemati- cal speculation, striking in its ambition and its formal beauty, but quite separated from the main stream of modern Physics, which had centered, after the early twenties, on quantum mechanics and its applications.

This book is devoted to an exposition of the theory of polynomially convex sets.

A comprehensive graduate-level introduction to classical and contemporary aspects of special functions.

Current and historical research methods in approximation theory are presented in this book beginning with the 1800s and following the evolution of approximation theory via the refinement and extension of classical methods and ending with recent techniques and methodologies.

This book is intended for advanced students and young researchers interested in the analysis of partial differential equations and differential geometry.

If H is a Hilbert space and T : H ?

A detailed treatment of potential theory on the real hyperbolic ball and half-space aimed at researchers and graduate students.

In many problems arising in engineering and science one requires approxi- tion methods to reproduce physical reality as well as possible.

This volume contains the contributions of the participants of the 14th ISAAC congress, held at the University of Sao Paulo, Campus Ribeirao Preto, Brazil, on July 17-21, 2023.

This volume presents research and expository papers highlighting the vibrant and fascinating study of irregularities in the distribution of primes.

Das Buch bietet eine vollständige Darstellung der Funktionentheorie, beginnend mit der Theorie der Riemann`schen Flächen einschließlich Uniformisierungstheorie sowie einer ausführlichen Darstellung der Theorie der kompakten Riemann`schen Flächen, Riemann-Roch`schem Satz, Abel`schem Theorem und Jacobi`schem Umkehrtheorem.

Dedicated to Anthony Joseph, this volume contains surveys and invited articles by leading specialists in representation theory.

Vitushkin's conjecture, a special case of Painleve's problem, states that a compact subset of the complex plane with finite linear Hausdorff measure is removable for bounded analytic functions if and only if it intersects every rectifiable curve in a set of zero arc length measure.

Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects.

A basic principle governing the boundary behaviour of holomorphic func- tions (and harmonic functions) is this: Under certain growth conditions, for almost every point in the boundary of the domain, these functions ad- mit a boundary limit, if we approach the bounda-ry point within certain approach regions.

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 is a valuable resource for Graduate students and researchers interested in current techniques and methods within the theory of moments in linear positive operators and approximation theory.

This volume contains a collection of research papers dedicated to Hans Grauert on the occasion of his seventieth birthday.

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

Originally published in 1999, Wavelets Made Easy offers a lucid and concise explanation of mathematical wavelets.

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

This book is the first to be devoted to the theory of vector-valued functions with one variable.

The book contains 13 articles, some of which are survey articles and others research papers.

This book consists of survey articles and original research papers in the representation theory of reductive p-adic groups.

Since its emergence as an important research area in the early 1980s, the topic of wavelets has undergone tremendous development on both theoretical and applied fronts.

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.

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).

The monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals.

Technological advancements in computing have changed how data is leveraged by businesses to develop, grow, and innovate.

Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space.

The second volume of the two volumes book is dedicated to various extensions and generalizations of Dyadic (Walsh) analysis and related applications.

The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.

This volume presents papers dedicated to Professor Shoshichi Kobayashi, commemorating the occasion of his sixtieth birthday on January 4, 1992.

A comprehensive graduate-level introduction to classical and contemporary aspects of special functions.

The first formulations of linear boundary value problems for analytic functions were due to Riemann (1857).

This self-contained text introduces Euclidean Fourier Analysis to graduate students who have completed courses in Real Analysis and Complex Variables.

The study of univalent functions dates back to the early years of the 20th century, and is one of the most popular research areas in complex analysis.

This volume is devoted to a systematic study of the Banach algebra of the convolution operators of a locally compact group.

In this book, the authors discuss the Mellin-Barnes representation of complex multidimensional integrals.

The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory.

This book is a short, but complete, introduction to the Loewner equation and the SLEs, which are a family of random fractal curves, as well as the relevant background in probability and complex analysis.