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Author : Philip J. Davis
Publisher : MAA Press
ISBN 13 :
Total Pages : 248 pages
Book Rating : 4.:/5 (5 download)
Download or read book The Schwarz Function and Its Applications written by Philip J. Davis and published by MAA Press. This book was released on 1974 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Philip J. Davis
Publisher : American Mathematical Soc.
ISBN 13 : 088385046X
Total Pages : 228 pages
Book Rating : 4.8/5 (838 download)
Download or read book The Schwarz Function and Its Applications written by Philip J. Davis and published by American Mathematical Soc.. This book was released on 1974-12-31 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: H. A. Schwarz showed us how to extend the notion of reflection in straight lines and circles to reflection in an arbitrary analytic arc. Notable applications were made to the symmetry principle and to problems of analytic continuation. Reflection, in the hands of Schwarz, is an antianalytic mapping. By taking its complex conjugate, we arrive at an analytic function that we have called here the Schwarz Function of the analytic arc. This function is worthy of study in its own right and this essay presents such a study. In dealing with certain familiar topics, the use of the Schwarz Function lends a point of view, a clarity and elegance, and a degree of generality which might otherwise be missing. It opens up a line of inquiry which has yielded numerous interesting things in complex variables; it illuminates some functional equations and a variety of iterations which interest the numerical analyst. The perceptive reader will certainly find here some old wine in relabelled bottles. But one of the principles of mathematical growth is that the relabelling process often suggests a new generation of problems. Means become ends; the medium rapidly becomes the message. This book is not wholly self-contained. Readers will find that they should be familiar with the elementary portions of linear algebra and of the theory of functions of a complex variable.
Author : Harold S. Shapiro
Publisher : John Wiley & Sons
ISBN 13 : 9780471571278
Total Pages : 126 pages
Book Rating : 4.5/5 (712 download)
Download or read book The Schwarz Function and Its Generalization to Higher Dimensions written by Harold S. Shapiro and published by John Wiley & Sons. This book was released on 1992-04-16 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Schwarz function originates in classical complex analysis and potential theory. Here the author presents the advantages favoring a mode of treatment which unites the subject with modern theory of distributions and partial differential equations thus bridging the gap between two-dimensional geometric and multi-dimensional analysts. Examines the Schwarz function and its relationship to recent investigations regarding inverse problems of Newtonian gravitation, free boundaries, Hele-Shaw flows and the propagation of singularities for holomorphic p.d.e.
Author : Philip J. Davis
Publisher : MAA Press
ISBN 13 :
Total Pages : 248 pages
Book Rating : 4.:/5 (5 download)
Download or read book The Schwarz Function and Its Applications written by Philip J. Davis and published by MAA Press. This book was released on 1974 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ilia Binder
Publisher : Springer Nature
ISBN 13 : 3031392701
Total Pages : 487 pages
Book Rating : 4.0/5 (313 download)
Download or read book Function Spaces, Theory and Applications written by Ilia Binder and published by Springer Nature. This book was released on 2024-01-12 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert spaces of analytic functions form one of the pillars of complex analysis. These spaces have a rich structure and for more than a century have been studied by many prominent mathematicians. They also have several essential applications in other fields of mathematics and engineering, e.g., robust control engineering, signal and image processing, and theory of communication. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins, e.g. the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b), have also been the center of attention in the past two decades. Studying the Hilbert spaces of analytic functions and the operators acting on them, as well as their applications in other parts of mathematics or engineering were the main subjects of this program. During the program, the world leading experts on function spaces gathered and discussed the new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains. With more than 250 hours of lectures by prominent mathematicians, a wide variety of topics were covered. More explicitly, there were mini-courses and workshops on Hardy Spaces, Dirichlet Spaces, Bergman Spaces, Model Spaces, Interpolation and Sampling, Riesz Bases, Frames and Signal Processing, Bounded Mean Oscillation, de Branges-Rovnyak Spaces, Operators on Function Spaces, Truncated Toeplitz Operators, Blaschke Products and Inner Functions, Discrete and Continuous Semigroups of Composition Operators, The Corona Problem, Non-commutative Function Theory, Drury-Arveson Space, and Convergence of Scattering Data and Non-linear Fourier Transform. At the end of each week, there was a high profile colloquium talk on the current topic. The program also contained two semester-long advanced courses on Schramm Loewner Evolution and Lattice Models and Reproducing Kernel Hilbert Space of Analytic Functions. The current volume features a more detailed version of some of the talks presented during the program.
Author : Alexander Vasil'ev
Publisher : Springer Science & Business Media
ISBN 13 : 331901806X
Total Pages : 364 pages
Book Rating : 4.3/5 (19 download)
Download or read book Harmonic and Complex Analysis and its Applications written by Alexander Vasil'ev and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume highlights the main results of the research performed within the network “Harmonic and Complex Analysis and its Applications” (HCAA), which was a five-year (2007–2012) European Science Foundation Programme intended to explore and to strengthen the bridge between two scientific communities: analysts with broad backgrounds in complex and harmonic analysis and mathematical physics, and specialists in physics and applied sciences. It coordinated actions for advancing harmonic and complex analysis and for expanding its application to challenging scientific problems. Particular topics considered by this Programme included conformal and quasiconformal mappings, potential theory, Banach spaces of analytic functions and their applications to the problems of fluid mechanics, conformal field theory, Hamiltonian and Lagrangian mechanics, and signal processing. This book is a collection of surveys written as a result of activities of the Programme and will be interesting and useful for professionals and novices in analysis and mathematical physics, as well as for graduate students. Browsing the volume, the reader will undoubtedly notice that, as the scope of the Programme is rather broad, there are many interrelations between the various contributions, which can be regarded as different facets of a common theme.
Author : Reiner Kuhnau
Publisher : Elsevier
ISBN 13 : 0080495176
Total Pages : 876 pages
Book Rating : 4.0/5 (84 download)
Download or read book Handbook of Complex Analysis written by Reiner Kuhnau and published by Elsevier. This book was released on 2004-12-09 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Function Theory is that part of Complex Analysis which covers the theory of conformal and quasiconformal mappings. Beginning with the classical Riemann mapping theorem, there is a lot of existence theorems for canonical conformal mappings. On the other side there is an extensive theory of qualitative properties of conformal and quasiconformal mappings, concerning mainly a prior estimates, so called distortion theorems (including the Bieberbach conjecture with the proof of the Branges). Here a starting point was the classical Scharz lemma, and then Koebe's distortion theorem. There are several connections to mathematical physics, because of the relations to potential theory (in the plane). The Handbook of Geometric Function Theory contains also an article about constructive methods and further a Bibliography including applications eg: to electroxtatic problems, heat conduction, potential flows (in the plane). · A collection of independent survey articles in the field of GeometricFunction Theory · Existence theorems and qualitative properties of conformal and quasiconformal mappings · A bibliography, including many hints to applications in electrostatics, heat conduction, potential flows (in the plane).
Author : Vladimir Kadets
Publisher : Elsevier
ISBN 13 : 008047280X
Total Pages : 342 pages
Book Rating : 4.0/5 (84 download)
Download or read book Functional Analysis and its Applications written by Vladimir Kadets and published by Elsevier. This book was released on 2004-07-31 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conference took place in Lviv, Ukraine and was dedicated to a famous Polish mathematician Stefan Banach ƒ{ the most outstanding representative of the Lviv mathematical school. Banach spaces, introduced by Stefan Banach at the beginning of twentieth century, are familiar now to every mathematician. The book contains a short historical article and scientific contributions of the conference participants, mostly in the areas of functional analysis, general topology, operator theory and related topics.
Author : Tristan Needham
Publisher : Oxford University Press
ISBN 13 : 9780198534464
Total Pages : 620 pages
Book Rating : 4.5/5 (344 download)
Download or read book Visual Complex Analysis written by Tristan Needham and published by Oxford University Press. This book was released on 1997 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.
Author : Carlos A. Berenstein
Publisher : Springer
ISBN 13 : 3540697020
Total Pages : 166 pages
Book Rating : 4.5/5 (46 download)
Download or read book Integral Geometry, Radon Transforms and Complex Analysis written by Carlos A. Berenstein and published by Springer. This book was released on 2006-11-14 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the notes of five short courses delivered at the "Centro Internazionale Matematico Estivo" session "Integral Geometry, Radon Transforms and Complex Analysis" held in Venice (Italy) in June 1996: three of them deal with various aspects of integral geometry, with a common emphasis on several kinds of Radon transforms, their properties and applications, the other two share a stress on CR manifolds and related problems. All lectures are accessible to a wide audience, and provide self-contained introductions and short surveys on the subjects, as well as detailed expositions of selected results.
Author : Mark Agranovsky
Publisher : Birkhäuser
ISBN 13 : 3319701541
Total Pages : 373 pages
Book Rating : 4.3/5 (197 download)
Download or read book Complex Analysis and Dynamical Systems written by Mark Agranovsky and published by Birkhäuser. This book was released on 2018-01-31 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on developments in complex dynamical systems and geometric function theory over the past decade, showing strong links with other areas of mathematics and the natural sciences. Traditional methods and approaches surface in physics and in the life and engineering sciences with increasing frequency – the Schramm‐Loewner evolution, Laplacian growth, and quadratic differentials are just a few typical examples. This book provides a representative overview of these processes and collects open problems in the various areas, while at the same time showing where and how each particular topic evolves. This volume is dedicated to the memory of Alexander Vasiliev.
Author : Eduardo Bayro Corrochano
Publisher : Springer Science & Business Media
ISBN 13 : 1461201594
Total Pages : 607 pages
Book Rating : 4.4/5 (612 download)
Download or read book Geometric Algebra with Applications in Science and Engineering written by Eduardo Bayro Corrochano and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science, and engineer ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar ticles here was pioneered in the 1960s by David Hestenes. Later, together with Garret Sobczyk, he developed it into a unified language for math ematics and physics. Sobczyk first learned about the power of geometric algebra in classes in electrodynamics and relativity taught by Hestenes at Arizona State University from 1966 to 1967. He still vividly remembers a feeling of disbelief that the fundamental geometric product of vectors could have been left out of his undergraduate mathematics education. Geometric algebra provides a rich, general mathematical framework for the develop ment of multilinear algebra, projective and affine geometry, calculus on a manifold, the representation of Lie groups and Lie algebras, the use of the horosphere and many other areas. This book is addressed to a broad audience of applied mathematicians, physicists, computer scientists, and engineers.
Author : Daniel Alpay
Publisher : Springer Science & Business Media
ISBN 13 : 3764373032
Total Pages : 323 pages
Book Rating : 4.7/5 (643 download)
Download or read book Operator Theory, Systems Theory and Scattering Theory: Multidimensional Generalizations written by Daniel Alpay and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of papers, from experts in the area, on multidimensional operator theory. Topics considered include the non-commutative case, function theory in the polydisk, hyponormal operators, hyperanalytic functions, and holomorphic deformations of linear differential equations. Operator Theory, Systems Theory and Scattering Theory will be of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.
Author : Makoto Sakai
Publisher : American Mathematical Soc.
ISBN 13 : 0821848100
Total Pages : 282 pages
Book Rating : 4.8/5 (218 download)
Download or read book Small Modifications of Quadrature Domains written by Makoto Sakai and published by American Mathematical Soc.. This book was released on 2010 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a given plane domain, the author adds a constant multiple of the Dirac measure at a point in the domain and makes a new domain called a quadrature domain. The quadrature domain is characterized as a domain such that the integral of a harmonic and integrable function over the domain equals the integral of the function over the given domain plus the integral of the function with respect to the added measure. The family of quadrature domains can be modeled as the Hele-Shaw flow with a free-boundary problem. The given domain is regarded as the initial domain and the support point of the Dirac measure as the injection point of the flow.
Author : H Begehr
Publisher : CRC Press
ISBN 13 : 1000951510
Total Pages : 286 pages
Book Rating : 4.0/5 (9 download)
Download or read book Transformations, Transmutations, and Kernel Functions, Volume II written by H Begehr and published by CRC Press. This book was released on 2023-06-16 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex analytical methods are a powerful tool for special partial differential equations and systems. To make these methods applicable for a wider class, transformations and transmutations are used.
Author : Thomas A. Garrity
Publisher : Cambridge University Press
ISBN 13 : 9780521797078
Total Pages : 378 pages
Book Rating : 4.7/5 (97 download)
Download or read book All the Mathematics You Missed written by Thomas A. Garrity and published by Cambridge University Press. This book was released on 2002 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: An essential resource for advanced undergraduate and beginning graduate students in quantitative subjects who need to quickly learn some serious mathematics.
Author : Ioannis Athanasopoulos
Publisher : Routledge
ISBN 13 : 1351447149
Total Pages : 366 pages
Book Rating : 4.3/5 (514 download)
Download or read book Free Boundary Problems written by Ioannis Athanasopoulos and published by Routledge. This book was released on 2019-11-11 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Free boundary problems arise in an enormous number of situations in nature and technology. They hold a strategic position in pure and applied sciences and thus have been the focus of considerable research over the last three decades. Free Boundary Problems: Theory and Applications presents the work and results of experts at the forefront of current research in mathematics, material sciences, chemical engineering, biology, and physics. It contains the plenary lectures and contributed papers of the 1997 International Interdisciplinary Congress proceedings held in Crete. The main topics addressed include free boundary problems in fluid and solid mechanics, combustion, the theory of filtration, and glaciology. Contributors also discuss material science modeling, recent mathematical developments, and numerical analysis advances within their presentations of more specific topics, such as singularities of interfaces, cusp cavitation and fracture, capillary fluid dynamics of film coating, dynamics of surface growth, phase transition kinetics, and phase field models. With the implications of free boundary problems so far reaching, it becomes important for researchers from all of these fields to stay abreast of new developments. Free Boundary Problems: Theory and Applications provides the opportunity to do just that, presenting recent advances from more than 50 researchers at the frontiers of science, mathematics, and technology.
