Distributions and the Boundary Values of Analytic Functions

Distributions and the Boundary Values of Analytic Functions

Author: E. J. Beltrami

Publisher: Academic Press

Published: 2014-05-12

Total Pages: 131

ISBN-13: 1483268101

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Distributions and the Boundary Values of Analytic Functions focuses on the tools and techniques of distribution theory and the distributional boundary behavior of analytic functions and their applications. The publication first offers information on distributions, including spaces of testing functions, distributions of finite order, convolution and regularization, and testing functions of rapid decay and distributions of slow growth. The text then examines Laplace transform, as well as Laplace transforms of distributions with arbitrary support. The manuscript ponders on distributional boundary values of analytic functions, including causal and passive operators, analytic continuation and uniqueness, boundary value theorems and generalized Hilbert transforms, and representation theorems for half-plane holomorphic functions with S' boundary behavior. The publication is a valuable source of data for researchers interested in distributions and the boundary values of analytic functions.


Boundary Values And Convolution In Ultradistribution Spaces

Boundary Values And Convolution In Ultradistribution Spaces

Author: Stevan Pilipovic

Publisher: World Scientific

Published: 2007-07-20

Total Pages: 230

ISBN-13: 9814475203

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This book provides the construction and characterization of important ultradistribution spaces and studies properties and calculations of ultradistributions such as boundedness and convolution. Integral transforms of ultradistributions are constructed and analyzed. The general theory of the representation of ultradistributions as boundary values of analytic functions is obtained and the recovery of the analytic functions as Cauchy, Fourier-Laplace, and Poisson integrals associated with the boundary value is proved.Ultradistributions are useful in applications in quantum field theory, partial differential equations, convolution equations, harmonic analysis, pseudo-differential theory, time-frequency analysis, and other areas of analysis. Thus this book is of interest to users of ultradistributions in applications as well as to research mathematicians in areas of analysis.


Hilbert Transforms: Volume 2

Hilbert Transforms: Volume 2

Author: Frederick W. King

Publisher: Cambridge University Press

Published: 2009-04-27

Total Pages: 661

ISBN-13: 0521517206

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The definitive reference on Hilbert transforms covering the mathematical techniques for evaluating them, and their application.


Passive Macromodeling

Passive Macromodeling

Author: Stefano Grivet-Talocia

Publisher: John Wiley & Sons

Published: 2015-12-07

Total Pages: 912

ISBN-13: 1118094913

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Offers an overview of state of the art passive macromodeling techniques with an emphasis on black-box approaches This book offers coverage of developments in linear macromodeling, with a focus on effective, proven methods. After starting with a definition of the fundamental properties that must characterize models of physical systems, the authors discuss several prominent passive macromodeling algorithms for lumped and distributed systems and compare them under accuracy, efficiency, and robustness standpoints. The book includes chapters with standard background material (such as linear time-invariant circuits and systems, basic discretization of field equations, state-space systems), as well as appendices collecting basic facts from linear algebra, optimization templates, and signals and transforms. The text also covers more technical and advanced topics, intended for the specialist, which may be skipped at first reading. Provides coverage of black-box passive macromodeling, an approach developed by the authors Elaborates on main concepts and results in a mathematically precise way using easy-to-understand language Illustrates macromodeling concepts through dedicated examples Includes a comprehensive set of end-of-chapter problems and exercises Passive Macromodeling: Theory and Applications serves as a reference for senior or graduate level courses in electrical engineering programs, and to engineers in the fields of numerical modeling, simulation, design, and optimization of electrical/electronic systems. Stefano Grivet-Talocia, PhD, is an Associate Professor of Circuit Theory at the Politecnico di Torino in Turin, Italy, and President of IdemWorks. Dr. Grivet-Talocia is author of over 150 technical papers published in international journals and conference proceedings. He invented several algorithms in the area of passive macromodeling, making them available through IdemWorks. Bjørn Gustavsen, PhD, is a Chief Research Scientist in Energy Systems at SINTEF Energy Research in Trondheim, Norway. More than ten years ago, Dr. Gustavsen developed the original version of the vector fitting method with Prof. Semlyen at the University of Toronto. The vector fitting method is one of the most widespread approaches for model extraction. Dr. Gustavsen is also an IEEE fellow.


Multidimensional Systems Theory and Applications

Multidimensional Systems Theory and Applications

Author: N.K. Bose

Publisher: Springer

Published: 2013-12-20

Total Pages: 282

ISBN-13: 9401702756

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The Second Edition of this book includes an abundance of examples to illustrate advanced concepts and brings out in a text book setting the algorithms for bivariate polynomial matrix factorization results that form the basis of two-dimensional systems theory. Algorithms and their implementation using symbolic algebra are emphasized.


Fourteen Papers Translated from the Russian

Fourteen Papers Translated from the Russian

Author: Ben Silver

Publisher: American Mathematical Soc.

Published: 1987-12-31

Total Pages: 170

ISBN-13: 9780821895726

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Covers a range of topics including integral representations, complex analysis, differential equations, and functional analysis.


Asymptotic Behavior of Generalized Functions

Asymptotic Behavior of Generalized Functions

Author: Stevan Pilipovic

Publisher: World Scientific

Published: 2012

Total Pages: 309

ISBN-13: 9814366854

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The asymptotic analysis has obtained new impulses with the general development of various branches of mathematical analysis and their applications. In this book, such impulses originate from the use of slowly varying functions and the asymptotic behavior of generalized functions. The most developed approaches related to generalized functions are those of Vladimirov, Drozhinov and Zavyalov, and that of Kanwal and Estrada. The first approach is followed by the authors of this book and extended in the direction of the S-asymptotics. The second approach OCo of Estrada, Kanwal and Vindas OCo is related to moment asymptotic expansions of generalized functions and the Ces''aro behavior. The main features of this book are the uses of strong methods of functional analysis and applications to the analysis of asymptotic behavior of solutions to partial differential equations, Abelian and Tauberian type theorems for integral transforms as well as for the summability of Fourier series and integrals. The book can be used by applied mathematicians, physicists, engineers and others who use classical asymptotic methods and wish to consider non-classical objects (generalized functions) and their asymptotics now in a more advanced setting.


Basic Complex Analysis

Basic Complex Analysis

Author: Barry Simon

Publisher: American Mathematical Soc.

Published: 2015-11-02

Total Pages: 661

ISBN-13: 1470411008

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A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 2A is devoted to basic complex analysis. It interweaves three analytic threads associated with Cauchy, Riemann, and Weierstrass, respectively. Cauchy's view focuses on the differential and integral calculus of functions of a complex variable, with the key topics being the Cauchy integral formula and contour integration. For Riemann, the geometry of the complex plane is central, with key topics being fractional linear transformations and conformal mapping. For Weierstrass, the power series is king, with key topics being spaces of analytic functions, the product formulas of Weierstrass and Hadamard, and the Weierstrass theory of elliptic functions. Subjects in this volume that are often missing in other texts include the Cauchy integral theorem when the contour is the boundary of a Jordan region, continued fractions, two proofs of the big Picard theorem, the uniformization theorem, Ahlfors's function, the sheaf of analytic germs, and Jacobi, as well as Weierstrass, elliptic functions.