The Schwarz Function And Its Applications

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The Schwarz Function And Its Applications

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Author : Philip J. Davis
language : en
Publisher: American Mathematical Soc.
Release Date : 1974-12-31

The Schwarz Function And Its Applications written by Philip J. Davis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-12-31 with Mathematics categories.

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.

Schwarz Function Its Applications

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Author : Philip J. Davis
language : en
Publisher: MAA Press
Release Date : 2014-05-10

Schwarz Function Its Applications written by Philip J. Davis and has been published by MAA Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Analytic functions categories.

Quadrature Domains And Their Applications

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Author : Peter Ebenfelt
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-10

Quadrature Domains And Their Applications written by Peter Ebenfelt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-10 with Mathematics categories.

Quadrature domains were singled out about 30 years ago by D. Aharonov and H.S. Shapiro in connection with an extremal problem in function theory. Since then, a series of coincidental discoveries put this class of planar domains at the center of crossroads of several quite independent mathematical theories, e.g., potential theory, Riemann surfaces, inverse problems, holomorphic partial differential equations, fluid mechanics, operator theory. The volume is devoted to recent advances in the theory of quadrature domains, illustrating well the multi-facet aspects of their nature. The book contains a large collection of open problems pertaining to the general theme of quadrature domains.

Harmonic And Complex Analysis And Its Applications

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Author : Alexander Vasil'ev
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-09

Harmonic And Complex Analysis And Its Applications written by Alexander Vasil'ev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-09 with Mathematics categories.

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.

Handbook Of Complex Analysis

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Author : Reiner Kuhnau
language : en
Publisher: Elsevier
Release Date : 2004-12-09

Handbook Of Complex Analysis written by Reiner Kuhnau and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-09 with Mathematics categories.

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).

Classical And Modern Potential Theory And Applications

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Author : K. GowriSankaran
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Classical And Modern Potential Theory And Applications written by K. GowriSankaran and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Proceedings of the NATO Advanced Research Workshop, Château de Bonas, France, July 25--31, 1993

Several Complex Variables And Complex Geometry Part Iii

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Author : Eric Bedford
language : en
Publisher: American Mathematical Soc.
Release Date : 1991

Several Complex Variables And Complex Geometry Part Iii written by Eric Bedford and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.

Complex Analysis And Dynamical Systems

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Author : Mark Agranovsky
language : en
Publisher: Birkhäuser
Release Date : 2018-01-31

Complex Analysis And Dynamical Systems written by Mark Agranovsky and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-31 with Mathematics categories.

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.

Nine Introductions In Complex Analysis Revised Edition

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Author : Sanford L. Segal
language : en
Publisher: Elsevier
Release Date : 2007-10-10

Nine Introductions In Complex Analysis Revised Edition written by Sanford L. Segal and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-10 with Mathematics categories.

The book addresses many topics not usually in "second course in complex analysis" texts. It also contains multiple proofs of several central results, and it has a minor historical perspective. - Proof of Bieberbach conjecture (after DeBranges) - Material on asymptotic values - Material on Natural Boundaries - First four chapters are comprehensive introduction to entire and metomorphic functions - First chapter (Riemann Mapping Theorem) takes up where "first courses" usually leave off

Complex Analysis And Dynamical Systems Vi

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Author : Lawrence Zalcman
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-05-19

Complex Analysis And Dynamical Systems Vi written by Lawrence Zalcman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-19 with Mathematics categories.

This volume contains the proceedings of the Sixth International Conference on Complex Analysis and Dynamical Systems, held from May 19–24, 2013, in Nahariya, Israel, in honor of David Shoikhet's sixtieth birthday. The papers range over a wide variety of topics in complex analysis, quasiconformal mappings, and complex dynamics. Taken together, the articles provide the reader with a panorama of activity in these areas, drawn by a number of leading figures in the field. They testify to the continued vitality of the interplay between classical and modern analysis. The companion volume (Contemporary Mathematics, Volume 653) is devoted to partial differential equations, differential geometry, and radon transforms.