Complex analysis, complex variables

This book provides an introduction into the modern theory of classical harmonic analysis, dealing with Fourier analysis and the most elementary singular integral operators, the Hilbert transform and Riesz transforms.

This monograph introduces a novel and effective approach to counting lattice paths by using the discrete Fourier transform (DFT) as a type of periodic generating function.

Dirac operators play an important role in several domains of mathematics and physics, for example: index theory, elliptic pseudodifferential operators, electromagnetism, particle physics, and the representation theory of Lie groups.

Helmholtz's seminal paper on vortex motion (1858) marks the beginning of what is now called topological fluid mechanics.

The idea of this book originated in the works presented at the First Latinamerican Conference on Mathematics in Industry and Medicine, held in Buenos Aires, Argentina, from November 27 to December 1, 1995.

The subject matter in this volume is Schwarz's Lemma which has become a crucial theme in many branches of research in mathematics for more than a hundred years to date.

This monograph examines rotation sets under the multiplication by d (mod 1) map and their relation to degree d polynomial maps of the complex plane.

The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics.

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

What is spectral action, how to compute it and what are the known examples?

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

This book offers a modern introduction to Nevanlinna theory and its intricate relation to the theory of normal families, algebraic functions, asymptotic series, and algebraic differential equations.

Princeton University's Elias Stein was the first mathematician to see the profound interconnections that tie classical Fourier analysis to several complex variables and representation theory.

Classical number theory is developed from scratch leading to geometric discrepancy theory, with Fourier analysis introduced along the way.

Modern Real and Complex Analysis Thorough, well-written, and encyclopedic in its coverage, this textoffers a lucid presentation of all the topics essential to graduatestudy in analysis.

The monograph is devoted to the use of the moduli method in mapping theory, in particular, the meaning of direct and inverse modulus inequalities and their possible applications.

The book describes developments on some well-known problems regarding the relationship between orders of finite groups and that of their automorphism groups.

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 second review volume is a follow-up to the book "e;Engineering of Chemical Complexity"e; that appeared in 2013.

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

This book presents a complete proof of Connes'' Index Theorem generalized to foliated spaces, including coverage of new developments and applications.

This second edition presents a collection of exercises on the theory of analytic functions, including completed and detailed solutions.

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 The book is the first formulation of a meta-philosophical scheme rooted in the embodied cognition paradigm.

Geometric Function Theory is a central part of Complex Analysis (one complex variable).

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.

This book provides a detailed study of recent results in metric fixed point theory and presents several applications in nonlinear analysis, including matrix equations, integral equations and polynomial approximations.

A careful and accessible exposition of functional analytic methods in stochastic analysis is provided in this book.

A revised and updated edition, providing hundreds of exercises to help students gradually transition from school to university-level calculus.

This text presents a collection of mathematical exercises with the aim of guiding readers to study topics in statistical physics, equilibrium thermodynamics, information theory, and their various connections.

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.

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

In [Hardy and Williams, 1986] the authors exploited a very simple idea to obtain a linear congruence involving class numbers of imaginary quadratic fields modulo a certain power of 2.

This workshop brought together specialists in complex analysis, differential geometry, mathematical physics and applications for stimulating cross-disciplinary discussions.

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.

Based on presentations given at the NordForsk Network Closing Conference "e;Operator Algebra and Dynamics,"e; held in Gjaargar ur, Faroe Islands, in May 2012, this book features high quality research contributions and review articles by researchers associated with the NordForsk network and leading experts that explore the fundamental role of operator algebras and dynamical systems in mathematics with possible applications to physics, engineering and computer science.

This contributed volume showcases the most significant results obtained from the DFG Priority Program on Compressed Sensing in Information Processing.

The monograph is devoted to the use of the moduli method in mapping theory, in particular, the meaning of direct and inverse modulus inequalities and their possible applications.

Harmonic analysis is a venerable part of modern mathematics.

This volume consists of 15 papers contributing to the Hayama Symposium on Complex Analysis in Several Variables XXIII, which was dedicated to the 100th anniversary of the creation of the Bergman kernel.

This book deals with the constructive Weierstrassian approach to the theory of function spaces and various applications.

The problems of conditional optimization of the uniform (or C-) norm for polynomials and rational functions arise in various branches of science and technology.