Singular Integrals and Fourier Theory on Lipschitz Boundaries


Book Description

The main purpose of this book is to provide a detailed and comprehensive survey of the theory of singular integrals and Fourier multipliers on Lipschitz curves and surfaces, an area that has been developed since the 1980s. The subject of singular integrals and the related Fourier multipliers on Lipschitz curves and surfaces has an extensive background in harmonic analysis and partial differential equations. The book elaborates on the basic framework, the Fourier methodology, and the main results in various contexts, especially addressing the following topics: singular integral operators with holomorphic kernels, fractional integral and differential operators with holomorphic kernels, holomorphic and monogenic Fourier multipliers, and Cauchy-Dunford functional calculi of the Dirac operators on Lipschitz curves and surfaces, and the high-dimensional Fueter mapping theorem with applications. The book offers a valuable resource for all graduate students and researchers interested in singular integrals and Fourier multipliers.




Mathematical Reviews


Book Description




Clifford Algebras and their Applications in Mathematical Physics


Book Description

This International Conference on Clifford AlgebrfU and Their Application, in Math ematical Phy,ic, is the third in a series of conferences on this theme, which started at the Univer,ity of Kent in Canterbury in 1985 and was continued at the Univer,iU de, Science, et Technique, du Languedoc in Montpellier in 1989. Since the start of this series of Conferences the research fields under consideration have evolved quite a lot. The number of scientific papers on Clifford Algebra, Clifford Analysis and their impact on the modelling of physics phenomena have increased tremendously and several new books on these topics were published. We were very pleased to see old friends back and to wellcome new guests who by their inspiring talks contributed fundamentally to tracing new paths for the future development of this research area. The Conference was organized in Deinze, a small rural town in the vicinity of the University town Gent. It was hosted by De Ceder, a vacation and seminar center in a green area, a typical landscape of Flanders's "plat pays" . The Conference was attended by 61 participants coming from 18 countries; there were 10 main talks on invitation, 37 contributions accepted by the Organizing Com mittee and a poster session. There was also a book display of Kluwer Academic Publishers. As in the Proceedings of the Canterbury and Montpellier conferences we have grouped the papers accordingly to the themes they are related to: Clifford Algebra, Clifford Analysis, Classical Mechanics, Mathematical Physics and Physics Models.




Clifford Algebras and their Applications in Mathematical Physics


Book Description

The second part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. from applications such as complex-distance potential theory, supersymmetry, and fluid dynamics to Fourier analysis, the study of boundary value problems, and applications, to mathematical physics and Schwarzian derivatives in Euclidean space. Among the mathematical topics examined are generalized Dirac operators, holonomy groups, monogenic and hypermonogenic functions and their derivatives, quaternionic Beltrami equations, Fourier theory under Mobius transformations, Cauchy-Reimann operators, and Cauchy type integrals.




The General Theory of Relativity


Book Description

The General Theory of Relativity: A Mathematical Exposition will serve readers as a modern mathematical introduction to the general theory of relativity. Throughout the book, examples, worked-out problems, and exercises (with hints and solutions) are furnished. Topics in this book include, but are not limited to: tensor analysis the special theory of relativity the general theory of relativity and Einstein’s field equations spherically symmetric solutions and experimental confirmations static and stationary space-time domains black holes cosmological models algebraic classifications and the Newman-Penrose equations the coupled Einstein-Maxwell-Klein-Gordon equations appendices covering mathematical supplements and special topics Mathematical rigor, yet very clear presentation of the topics make this book a unique text for both university students and research scholars. Anadijiban Das has taught courses on Relativity Theory at The University College of Dublin, Ireland, Jadavpur University, India, Carnegie-Mellon University, USA, and Simon Fraser University, Canada. His major areas of research include, among diverse topics, the mathematical aspects of general relativity theory. Andrew DeBenedictis has taught courses in Theoretical Physics at Simon Fraser University, Canada, and is also a member of The Pacific Institute for the Mathematical Sciences. His research interests include quantum gravity, classical gravity, and semi-classical gravity.




Timelines of Nearly Everything


Book Description

This book takes readers back and forth through time and makes the past accessible to all families, students and the general reader and is an unprecedented collection of a list of events in chronological order and a wealth of informative knowledge about the rise and fall of empires, major scientific breakthroughs, groundbreaking inventions, and monumental moments about everything that has ever happened.




Advancements in Complex Analysis


Book Description

The contributions to this volume are devoted to a discussion of state-of-the-art research and treatment of problems of a wide spectrum of areas in complex analysis ranging from pure to applied and interdisciplinary mathematical research. Topics covered include: holomorphic approximation, hypercomplex analysis, special functions of complex variables, automorphic groups, zeros of the Riemann zeta function, Gaussian multiplicative chaos, non-constant frequency decompositions, minimal kernels, one-component inner functions, power moment problems, complex dynamics, biholomorphic cryptosystems, fermionic and bosonic operators. The book will appeal to graduate students and research mathematicians as well as to physicists, engineers, and scientists, whose work is related to the topics covered.




Function Spaces and Applications


Book Description

This seminar is a loose continuation of two previous conferences held in Lund (1982, 1983), mainly devoted to interpolation spaces, which resulted in the publication of the Lecture Notes in Mathematics Vol. 1070. This explains the bias towards that subject. The idea this time was, however, to bring together mathematicians also from other related areas of analysis. To emphasize the historical roots of the subject, the collection is preceded by a lecture on the life of Marcel Riesz.




Blaschke Products and Their Applications


Book Description

​Blaschke Products and Their Applications presents a collection of survey articles that examine Blaschke products and several of its applications to fields such as approximation theory, differential equations, dynamical systems, harmonic analysis, to name a few. Additionally, this volume illustrates the historical roots of Blaschke products and highlights key research on this topic. For nearly a century, Blaschke products have been researched. Their boundary behaviour, the asymptomatic growth of various integral means and their derivatives, their applications within several branches of mathematics, and their membership in different function spaces and their dynamics, are a few examples of where Blaschke products have shown to be important. The contributions written by experts from various fields of mathematical research will engage graduate students and researches alike, bringing the reader to the forefront of research in the topic. The readers will also discover the various open problems, enabling them to better pursue their own research.




Hypercomplex Analysis: New Perspectives and Applications


Book Description

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. In recent decades this theory has come to the forefront of higher dimensional analysis. There are several approaches to this: quaternionic analysis which merely uses quaternions, Clifford analysis which relies on Clifford algebras, and generalizations of complex variables to higher dimensions such as split-complex variables. This book includes a selection of papers presented at the session on quaternionic and hypercomplex analysis at the ISAAC conference 2013 in Krakow, Poland. The topics covered represent new perspectives and current trends in hypercomplex analysis and applications to mathematical physics, image analysis and processing, and mechanics.