Finding Ellipses What Blaschke Products Poncelets Theorem And The Numerical Range Know About Each Other

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Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other

Author : Ulrich Daepp
Publisher : American Mathematical Soc.
ISBN 13 : 147044383X
Total Pages : 268 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other by : Ulrich Daepp

Download or read book Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other written by Ulrich Daepp and published by American Mathematical Soc.. This book was released on 2018 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians delight in finding surprising connections between seemingly disparate areas of mathematics. Whole domains of modern mathematics have arisen from exploration of such connections--consider analytic number theory or algebraic topology. Finding Ellipses is a delight-filled romp across a three-way unexpected connection between complex analysis, linear algebra, and projective geometry. The book begins with Blaschke products, complex-analytic functions that are generalizations of disk automorphisms. In the analysis of Blaschke products, we encounter, in a quite natural way, an ellipse inside the unit disk. The story continues by introducing the reader to Poncelet's theorem--a beautiful result in projective geometry that ties together two conics and, in particular, two ellipses, one circumscribed by a polygon that is inscribed in the second. The Blaschke ellipse and the Poncelet ellipse turn out to be the same ellipse, and the connection is illuminated by considering the numerical range of a $2 \times 2$ matrix. The numerical range is a convex subset of the complex plane that contains information about the geometry of the transformation represented by a matrix. Through the numerical range of $n \times n$ matrices, we learn more about the interplay between Poncelet's theorem and Blaschke products. The story ranges widely over analysis, algebra, and geometry, and the exposition of the deep and surprising connections is lucid and compelling. Written for advanced undergraduates or beginning graduate students, this book would be the perfect vehicle for an invigorating and enlightening capstone exploration. The exercises and collection of extensive projects could be used as an embarkation point for a satisfying and rich research project. You are invited to read actively using the accompanying interactive website, which allows you to visualize the concepts in the book, experiment, and develop original conjectures.

Function Theory on Symplectic Manifolds

Author : Leonid Polterovich
Publisher : American Mathematical Soc.
ISBN 13 : 147041693X
Total Pages : 282 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Function Theory on Symplectic Manifolds by : Leonid Polterovich

Download or read book Function Theory on Symplectic Manifolds written by Leonid Polterovich and published by American Mathematical Soc.. This book was released on 2014 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book on symplectic topology, a rapidly developing field of mathematics which originated as a geometric tool for problems of classical mechanics. Since the 1980s, powerful methods such as Gromov's pseudo-holomorphic curves and Morse-Floer theory on loop spaces gave rise to the discovery of unexpected symplectic phenomena. The present book focuses on function spaces associated with a symplectic manifold. A number of recent advances show that these spaces exhibit intriguing properties and structures, giving rise to an alternative intuition and new tools in symplectic topology. The book provides an essentially self-contained introduction into these developments along with applications to symplectic topology, algebra and geometry of symplectomorphism groups, Hamiltonian dynamics and quantum mechanics. It will appeal to researchers and students from the graduate level onwards.

Operator and Matrix Theory, Function Spaces, and Applications

Author : Marek Ptak
Publisher : Springer Nature
ISBN 13 : 3031506138
Total Pages : 423 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Operator and Matrix Theory, Function Spaces, and Applications by : Marek Ptak

Download or read book Operator and Matrix Theory, Function Spaces, and Applications written by Marek Ptak and published by Springer Nature. This book was released on with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Complex Analysis and Spectral Theory

Author : H. Garth Dales
Publisher : American Mathematical Soc.
ISBN 13 : 1470446928
Total Pages : 280 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Complex Analysis and Spectral Theory by : H. Garth Dales

Download or read book Complex Analysis and Spectral Theory written by H. Garth Dales and published by American Mathematical Soc.. This book was released on 2020-02-07 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Conference on Complex Analysis and Spectral Theory, in celebration of Thomas Ransford's 60th birthday, held from May 21–25, 2018, at Laval University, Québec, Canada. Spectral theory is the branch of mathematics devoted to the study of matrices and their eigenvalues, as well as their infinite-dimensional counterparts, linear operators and their spectra. Spectral theory is ubiquitous in science and engineering because so many physical phenomena, being essentially linear in nature, can be modelled using linear operators. On the other hand, complex analysis is the calculus of functions of a complex variable. They are widely used in mathematics, physics, and in engineering. Both topics are related to numerous other domains in mathematics as well as other branches of science and engineering. The list includes, but is not restricted to, analytical mechanics, physics, astronomy (celestial mechanics), geology (weather modeling), chemistry (reaction rates), biology, population modeling, economics (stock trends, interest rates and the market equilibrium price changes). There are many other connections, and in recent years there has been a tremendous amount of work on reproducing kernel Hilbert spaces of analytic functions, on the operators acting on them, as well as on applications in physics and engineering, which arise from pure topics like interpolation and sampling. Many of these connections are discussed in articles included in this book.

From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory

Author : Fritz Gesztesy
Publisher : Springer Nature
ISBN 13 : 3030754251
Total Pages : 388 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory by : Fritz Gesztesy

Download or read book From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory written by Fritz Gesztesy and published by Springer Nature. This book was released on 2021-11-11 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topics of this volume, dedicated to Lance Littlejohn, are operator and spectral theory, orthogonal polynomials, combinatorics, number theory, and the various interplays of these subjects. Although the event, originally scheduled as the Baylor Analysis Fest, had to be postponed due to the pandemic, scholars from around the globe have contributed research in a broad range of mathematical fields. The collection will be of interest to both graduate students and professional mathematicians. Contributors are: G.E. Andrews, B.M. Brown, D. Damanik, M.L. Dawsey, W.D. Evans, J. Fillman, D. Frymark, A.G. García, L.G. Garza, F. Gesztesy, D. Gómez-Ullate, Y. Grandati, F.A. Grünbaum, S. Guo, M. Hunziker, A. Iserles, T.F. Jones, K. Kirsten, Y. Lee, C. Liaw, F. Marcellán, C. Markett, A. Martinez-Finkelshtein, D. McCarthy, R. Milson, D. Mitrea, I. Mitrea, M. Mitrea, G. Novello, D. Ong, K. Ono, J.L. Padgett, M.M.M. Pang, T. Poe, A. Sri Ranga, K. Schiefermayr, Q. Sheng, B. Simanek, J. Stanfill, L. Velázquez, M. Webb, J. Wilkening, I.G. Wood, M. Zinchenko.

Recent Progress in Function Theory and Operator Theory

Author : Alberto A. Condori
Publisher : American Mathematical Society
ISBN 13 : 1470472465
Total Pages : 226 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Recent Progress in Function Theory and Operator Theory by : Alberto A. Condori

Download or read book Recent Progress in Function Theory and Operator Theory written by Alberto A. Condori and published by American Mathematical Society. This book was released on 2024-04-30 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Recent Progress in Function Theory and Operator Theory, held virtually on April 6, 2022. Function theory is a classical subject that examines the properties of individual elements in a function space, while operator theory usually deals with concrete operators acting on such spaces or other structured collections of functions. These topics occupy a central position in analysis, with important connections to partial differential equations, spectral theory, approximation theory, and several complex variables. With the aid of certain canonical representations or “models”, the study of general operators can often be reduced to that of the operator of multiplication by one or several independent variables, acting on spaces of analytic functions or compressions of this operator to co-invariant subspaces. In this way, a detailed understanding of operators becomes connected with natural questions concerning analytic functions, such as zero sets, constructions of functions constrained by norms or interpolation, multiplicative structures granted by factorizations in spaces of analytic functions, and so forth. In many cases, non-obvious problems initially motivated by operator-theoretic considerations turn out to be interesting on their own, leading to unexpected challenges in function theory. The research papers in this volume deal with the interplay between function theory and operator theory and the way in which they influence each other.

Geometry of Polynomials

Author : Morris Marden
Publisher : American Mathematical Soc.
ISBN 13 : 0821815032
Total Pages : 260 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometry of Polynomials by : Morris Marden

Download or read book Geometry of Polynomials written by Morris Marden and published by American Mathematical Soc.. This book was released on 1949-12-31 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the years since the first edition of this well-known monograph appeared, the subject (the geometry of the zeros of a complex polynomial) has continued to display the same outstanding vitality as it did in the first 150 years of its history, beginning with the contributions of Cauchy and Gauss. Thus, the number of entries in the bibliography of this edition had to be increased from about 300 to about 600 and the book enlarged by one third. It now includes a more extensive treatment of Hurwitz polynomials and other topics. The new material on infrapolynomials, abstract polynomials, and matrix methods is of particular interest.

Geometry in History

Author : S. G. Dani
Publisher : Springer Nature
ISBN 13 : 3030136094
Total Pages : 759 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Geometry in History by : S. G. Dani

Download or read book Geometry in History written by S. G. Dani and published by Springer Nature. This book was released on 2019-10-18 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.

Finite Blaschke Products and Their Connections

Author : Stephan Ramon Garcia
Publisher : Springer
ISBN 13 : 3319782479
Total Pages : 328 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Finite Blaschke Products and Their Connections by : Stephan Ramon Garcia

Download or read book Finite Blaschke Products and Their Connections written by Stephan Ramon Garcia and published by Springer. This book was released on 2018-05-24 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph offers an introduction to finite Blaschke products and their connections to complex analysis, linear algebra, operator theory, matrix analysis, and other fields. Old favorites such as the Carathéodory approximation and the Pick interpolation theorems are featured, as are many topics that have never received a modern treatment, such as the Bohr radius and Ritt's theorem on decomposability. Deep connections to hyperbolic geometry are explored, as are the mapping properties, zeros, residues, and critical points of finite Blaschke products. In addition, model spaces, rational functions with real boundary values, spectral mapping properties of the numerical range, and the Darlington synthesis problem from electrical engineering are also covered. Topics are carefully discussed, and numerous examples and illustrations highlight crucial ideas. While thorough explanations allow the reader to appreciate the beauty of the subject, relevant exercises following each chapter improve technical fluency with the material. With much of the material previously scattered throughout mathematical history, this book presents a cohesive, comprehensive and modern exposition accessible to undergraduate students, graduate students, and researchers who have familiarity with complex analysis.

Leonhard Euler

Author : Robert E. Bradley
Publisher : Elsevier
ISBN 13 : 0080471293
Total Pages : 543 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Leonhard Euler by : Robert E. Bradley

Download or read book Leonhard Euler written by Robert E. Bradley and published by Elsevier. This book was released on 2007-03-20 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: The year 2007 marks the 300th anniversary of the birth of one of the Enlightenment’s most important mathematicians and scientists, Leonhard Euler. This volume is a collection of 24 essays by some of the world’s best Eulerian scholars from seven different countries about Euler, his life and his work. Some of the essays are historical, including much previously unknown information about Euler’s life, his activities in the St. Petersburg Academy, the influence of the Russian Princess Dashkova, and Euler’s philosophy. Others describe his influence on the subsequent growth of European mathematics and physics in the 19th century. Still others give technical details of Euler’s innovations in probability, number theory, geometry, analysis, astronomy, mechanics and other fields of mathematics and science. - Over 20 essays by some of the best historians of mathematics and science, including Ronald Calinger, Peter Hoffmann, Curtis Wilson, Kim Plofker, Victor Katz, Ruediger Thiele, David Richeson, Robin Wilson, Ivor Grattan-Guinness and Karin Reich- New details of Euler's life in two essays, one by Ronald Calinger and one he co-authored with Elena Polyakhova- New information on Euler's work in differential geometry, series, mechanics, and other important topics including his influence in the early 19th century

Reading, Writing, and Proving

Author : Ulrich Daepp
Publisher : Springer Science & Business Media
ISBN 13 : 0387215603
Total Pages : 391 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Reading, Writing, and Proving by : Ulrich Daepp

Download or read book Reading, Writing, and Proving written by Ulrich Daepp and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, based on Pólya's method of problem solving, aids students in their transition to higher-level mathematics. It begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics and ends by providing projects for independent study. Students will follow Pólya's four step process: learn to understand the problem; devise a plan to solve the problem; carry out that plan; and look back and check what the results told them.

Automated Deduction in Geometry

Author : Xiao-lu Gao
Publisher : Springer
ISBN 13 : 354047997X
Total Pages : 292 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Automated Deduction in Geometry by : Xiao-lu Gao

Download or read book Automated Deduction in Geometry written by Xiao-lu Gao and published by Springer. This book was released on 2003-06-26 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Second International Workshop on Automated Deduction in Geometry (ADG ’98) was held in Beijing, China, August 1–3, 1998. An increase of interest in ADG ’98 over the previous workshop ADG ’96 is represented by the notable number of more than 40 participants from ten countries and the strong tech- cal program of 25 presentations, of which two one-hour invited talks were given by Professors Wen-tsun ̈ Wu and Jing-Zhong Zhang. The workshop provided the participants with a well-focused forum for e?ective exchange of new ideas and timely report of research progress. Insight surveys, algorithmic developments, and applications in CAGD/CAD and computer vision presented by active - searchers, together with geometry software demos, shed light on the features of this second workshop. ADG ’98 was hosted by the Mathematics Mechanization Research Center (MMRC) with ?nancial support from the Chinese Academy of Sciences and the French National Center for Scienti?c Research (CNRS), and was organized by the three co-editors of this proceedings volume. The papers contained in the volume were selected, under a strict refereeing procedure, from those presented at ADG ’98 and submitted afterwards. Most of the 14 accepted papers were carefully revised and some of the revised versions were checked again by external reviewers. We hope that these papers cover some of the most recent and signi?cant research results and developments and re?ect the current state-of-the-art of ADG.

Poncelet Porisms and Beyond

Author : Vladimir Dragović
Publisher : Springer Science & Business Media
ISBN 13 : 3034800150
Total Pages : 293 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Poncelet Porisms and Beyond by : Vladimir Dragović

Download or read book Poncelet Porisms and Beyond written by Vladimir Dragović and published by Springer Science & Business Media. This book was released on 2011-05-02 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to present, in a complete and comprehensive way, areas of current research interlacing around the Poncelet porism: dynamics of integrable billiards, algebraic geometry of hyperelliptic Jacobians, and classical projective geometry of pencils of quadrics. The most important results and ideas, classical as well as modern, connected to the Poncelet theorem are presented, together with a historical overview analyzing the classical ideas and their natural generalizations. Special attention is paid to the realization of the Griffiths and Harris programme about Poncelet-type problems and addition theorems. This programme, formulated three decades ago, is aimed to understanding the higher-dimensional analogues of Poncelet problems and the realization of the synthetic approach of higher genus addition theorems.

Descriptive Geometry, The Spread of a Polytechnic Art

Author : Évelyne Barbin
Publisher : Springer
ISBN 13 : 3030148084
Total Pages : 437 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Descriptive Geometry, The Spread of a Polytechnic Art by : Évelyne Barbin

Download or read book Descriptive Geometry, The Spread of a Polytechnic Art written by Évelyne Barbin and published by Springer. This book was released on 2019-07-01 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book seeks to explore the history of descriptive geometry in relation to its circulation in the 19th century, which had been favoured by the transfers of the model of the École Polytechnique to other countries. The book also covers the diffusion of its teaching from higher instruction to technical and secondary teaching. In relation to that, there is analysis of the role of the institution – similar but definitely not identical in the different countries – in the field under consideration. The book contains chapters focused on different countries, areas, and institutions, written by specialists of the history of the field. Insights on descriptive geometry are provided in the context of the mathematical aspect, the aspect of teaching in particular to non-mathematicians, and the institutions themselves.

Blaschke Products and Their Applications

Author : Javad Mashreghi
Publisher : Springer Science & Business Media
ISBN 13 : 1461453402
Total Pages : 324 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Blaschke Products and Their Applications by : Javad Mashreghi

Download or read book Blaschke Products and Their Applications written by Javad Mashreghi and published by Springer Science & Business Media. This book was released on 2012-10-05 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Blaschke Products

Author : Peter Colwell
Publisher :
ISBN 13 : 9780472750795
Total Pages : 0 pages
Book Rating : 4.7/5 (57 download)

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Book Synopsis Blaschke Products by : Peter Colwell

Download or read book Blaschke Products written by Peter Colwell and published by . This book was released on 2016-10-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Blaschke products are an important class of functions in analytic function theory in the unit disk, both because of their involvement in factorization theorems and their utility for the construction of examples. This book gathers the principal results about Blaschke products heretofore scattered in research papers over the past 70 years and provides an extensive bibliography of over 300 items. It is hoped that research workers in and students of function theory will find the book a useful guide and reference to the subject of Blaschke products.

The Advanced Geometry of Plane Curves and Their Applications

Author : C. Zwikker
Publisher : Courier Corporation
ISBN 13 : 0486153436
Total Pages : 316 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis The Advanced Geometry of Plane Curves and Their Applications by : C. Zwikker

Download or read book The Advanced Geometry of Plane Curves and Their Applications written by C. Zwikker and published by Courier Corporation. This book was released on 2011-11-30 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Of chief interest to mathematicians, but physicists and others will be fascinated ... and intrigued by the fruitful use of non-Cartesian methods. Students ... should find the book stimulating." — British Journal of Applied Physics This study of many important curves, their geometrical properties, and their applications features material not customarily treated in texts on synthetic or analytic Euclidean geometry. Its wide coverage, which includes both algebraic and transcendental curves, extends to unusual properties of familiar curves along with the nature of lesser known curves. Informative discussions of the line, circle, parabola, ellipse, and hyperbola presuppose only the most elementary facts. The less common curves — cissoid, strophoid, spirals, the leminscate, cycloid, epicycloid, cardioid, and many others — receive introductions that explain both their basic and advanced properties. Derived curves-the involute, evolute, pedal curve, envelope, and orthogonal trajectories-are also examined, with definitions of their important applications. These range through the fields of optics, electric circuit design, hydraulics, hydrodynamics, classical mechanics, electromagnetism, crystallography, gear design, road engineering, orbits of subatomic particles, and similar areas in physics and engineering. The author represents the points of the curves by complex numbers, rather than the real Cartesian coordinates, an approach that permits simple, direct, and elegant proofs.