Complex analysis, complex variables

Fractional calculus is used to model many real-life situations from science and engineering.

Fractional calculus is used to model many real-life situations from science and engineering.

The aim of this comparatively short textbook is a sufficiently full exposition of the fundamentals of the theory of functions of a complex variable to prepare the student for various applications.

The aim of this comparatively short textbook is a sufficiently full exposition of the fundamentals of the theory of functions of a complex variable to prepare the student for various applications.

Far from being separate entities, many social and engineering systems can be considered as complex network systems (CNSs) associated with closely linked interactions with neighbouring entities such as the Internet and power grids.

Far from being separate entities, many social and engineering systems can be considered as complex network systems (CNSs) associated with closely linked interactions with neighbouring entities such as the Internet and power grids.

Bringing together two fundamental texts from Frederic Pham's research on singular integrals, the first part of this book focuses on topological and geometrical aspects while the second explains the analytic approach.

This book provides an introduction to complex analysis in several variables.

Increasingly important in the field of communications, the study of time and band limiting is crucial for the modeling and analysis of multiband signals.

Sampling, wavelets, and tomography are three active areas of contemporary mathematics sharing common roots that lie at the heart of harmonic and Fourier analysis.

Dedicated to Jacques Carmona, an expert in noncommutative harmonic analysis, the volume presents excellent invited/refereed articles by top notch mathematicians.

Over the course of the last century, the systematic exploration of the relationship between Fourier analysis and other branches of mathematics has lead to important advances in geometry, number theory, and analysis, stimulated in part by Hurwitz's proof of the isoperimetric inequality using Fourier series.

One of the great successes of twentieth century mathematics has been the remarkable qualitative understanding of rational and integral points on curves, gleaned in part through the theorems of Mordell, Weil, Siegel, and Faltings.

In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer- sity of Cambridge.

It is a pleasure and a privilege to write this new edition of A Primer 0/ Real Ana- lytic Functions.

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.

With each methodology treated in its own chapter, this monograph is a thorough exploration of several theories that can be used to find explicit formulas for heat kernels for both elliptic and sub-elliptic operators.

This book deals with two subjects.

All modem introductions to complex analysis follow, more or less explicitly, the pattern laid down in Whittaker and Watson [75].

This state-of-the-art textbook covers four research directions in harmonic analysis and presents some of its latest applications.

The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the engineering, mathematical, and scienti?

The subjects of stochastic processes, information theory, and Lie groups are usually treated separately from each other.

This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century.

This text takes advantage of recent developments in the theory of path integration to provide an improved treatment of quantization of systems that either have no constraints or instead involve constraints with demonstratively improved procedures.

This volume, following in the tradition of a similar 2010 publication by the same editors, is an outgrowth of an international conference, "e;Fractals and Related Fields II,"e; held in June 2011.

The Norbert Wiener Center for Harmonic Analysis and Applications provides a state-of-the-art research venue for the broad emerging area of mathematical engineering in the context of harmonic analysis.

The Norbert Wiener Center for Harmonic Analysis and Applications provides a state-of-the-art research venue for the broad emerging area of mathematical engineering in the context of harmonic analysis.

Broadly organized around the applications of Fourier analysis, Methods of Applied Mathematics with a MATLAB Overview covers both classical applications in partial differential equations and boundary value problems, as well as the concepts and methods associated to the Laplace, Fourier, and discrete transforms.

The topics in this research monograph are at the interface of several areas of mathematics such as harmonic analysis, functional analysis, analysis on spaces of homogeneous type, topology, and quasi-metric geometry.

Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics.

This monograph isdevoted to a special area ofBanach space theory-the Kothe- Bochner function space.

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.

The classical subject of bases in Banach spaces has taken on a new life in the modern development of applied harmonic analysis.

Representations, Wavelets, and Frames contains chapters pertaining to this theme from experts and expositors of renown in mathematical analysis and representation theory.

Based on a streamlined presentation of the author's previous work, An Introduction to Frames and Riesz Bases, this new textbook fills a gap in the literature, developing frame theory as part of a dialogue between mathematicians and engineers.

Harmonic analysis is a venerable part of modern mathematics.

This textbook is an introduction to the theory and applications of finite tight frames, an area that has developed rapidly in the last decade.

This book introduces geometric spectral theory in the context of Riemann surfaces.

This work examines a rich tapestry of themes and concepts and provides a comprehensive treatment of an important area of mathematics, while simultaneously covering a broader area of the geometry of domains in complex space.

This self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables.

A collection of invited chapters dedicated to Carlos Segovia, this unified and self-contained volume examines recent developments in real and harmonic analysis.

The term convexity used to describe these lectures given at the Univer- sity of Lund in 1991-92 should be understood in a wide sense.

The second in a series of three volumes surveying the theory of theta functions, this volume gives emphasis to the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations as well as other non-linear differential equations of mathematical physics.

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

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

The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the engineering, mathematical, and scienti?

More than ten years have passed since the book of F.

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

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

Complex numbers can be viewed in several ways: as an element in a field, as a point in the plane, and as a two-dimensional vector.