From Divergent Power Series To Analytic Functions

Author : Werner Balser
Publisher : Springer
ISBN 13 : 3540485945
Total Pages : 117 pages
Book Rating : 4.40/5 ( download)

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Download or read book From Divergent Power Series to Analytic Functions written by Werner Balser and published by Springer. This book was released on 2006-11-15 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multisummability is a method which, for certain formal power series with radius of convergence equal to zero, produces an analytic function having the formal series as its asymptotic expansion. This book presents the theory of multisummabi- lity, and as an application, contains a proof of the fact that all formal power series solutions of non-linear meromorphic ODE are multisummable. It will be of use to graduate students and researchers in mathematics and theoretical physics, and especially to those who encounter formal power series to (physical) equations with rapidly, but regularly, growing coefficients.

Author : Werner Balser
Publisher :
ISBN 13 : 9783662187739
Total Pages : 124 pages
Book Rating : 4.36/5 ( download)

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Download or read book From Divergent Power Series to Analytic Functions written by Werner Balser and published by . This book was released on 2014-01-15 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Michèle Loday-Richaud
Publisher : Springer
ISBN 13 : 3319290754
Total Pages : 272 pages
Book Rating : 4.51/5 ( download)

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Download or read book Divergent Series, Summability and Resurgence II written by Michèle Loday-Richaud and published by Springer. This book was released on 2016-06-28 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addressing the question how to “sum” a power series in one variable when it diverges, that is, how to attach to it analytic functions, the volume gives answers by presenting and comparing the various theories of k-summability and multisummability. These theories apply in particular to all solutions of ordinary differential equations. The volume includes applications, examples and revisits, from a cohomological point of view, the group of tangent-to-identity germs of diffeomorphisms of C studied in volume 1. With a view to applying the theories to solutions of differential equations, a detailed survey of linear ordinary differential equations is provided, which includes Gevrey asymptotic expansions, Newton polygons, index theorems and Sibuya’s proof of the meromorphic classification theorem that characterizes the Stokes phenomenon for linear differential equations. This volume is the second in a series of three, entitled Divergent Series, Summability and Resurgence. It is aimed at graduate students and researchers in mathematics and theoretical physics who are interested in divergent series, Although closely related to the other two volumes, it can be read independently.

Author : Werner Balser
Publisher : Springer Science & Business Media
ISBN 13 : 0387986901
Total Pages : 314 pages
Book Rating : 4.06/5 ( download)

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Download or read book Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations written by Werner Balser and published by Springer Science & Business Media. This book was released on 2000 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simple Ordinary Differential Equations may have solutions in terms of power series whose coefficients grow at such a rate that the series has a radius of convergence equal to zero. In fact, every linear meromorphic system has a formal solution of a certain form, which can be relatively easily computed, but which generally involves such power series diverging everywhere. In this book the author presents the classical theory of meromorphic systems of ODE in the new light shed upon it by the recent achievements in the theory of summability of formal power series.

Author : Wolfgang Arendt
Publisher : John Wiley & Sons
ISBN 13 : 3527628037
Total Pages : 502 pages
Book Rating : 4.32/5 ( download)

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Download or read book Mathematical Analysis of Evolution, Information, and Complexity written by Wolfgang Arendt and published by John Wiley & Sons. This book was released on 2009-07-10 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Analysis of Evolution, Information, and Complexity deals with the analysis of evolution, information and complexity. The time evolution of systems or processes is a central question in science, this text covers a broad range of problems including diffusion processes, neuronal networks, quantum theory and cosmology. Bringing together a wide collection of research in mathematics, information theory, physics and other scientific and technical areas, this new title offers elementary and thus easily accessible introductions to the various fields of research addressed in the book.

Author : William Johnston
Publisher : OUP USA
ISBN 13 : 0195310764
Total Pages : 766 pages
Book Rating : 4.64/5 ( download)

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Download or read book A Transition to Advanced Mathematics written by William Johnston and published by OUP USA. This book was released on 2009-07-27 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface 1. Mathematical Logic 2. Abstract Algebra 3. Number Theory 4. Real Analysis 5. Probability and Statistics 6. Graph Theory 7. Complex Analysis Answers to Questions Answers to Odd Numbered Questions Index of Online Resources Bibliography Index.

Author : S. Saitoh
Publisher : Springer Science & Business Media
ISBN 13 : 1475729871
Total Pages : 235 pages
Book Rating : 4.70/5 ( download)

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Download or read book Reproducing Kernels and their Applications written by S. Saitoh and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: The First International Congress of the International Society for Analysis, its Applications and Computations (ISAAC'97) was held at the University of Delaware from 3 to 7 June 1997. As specified in the invitation of the President Professor Robert P. Gilbert of the ISAAC, we organized the session on Reproducing Kerneis and Their Applications. In our session, we presented 24 engaging talks on topics of current interest to the research community. As suggested and organized by Professor Gilbert, we hereby publish its Proceedings. Rather than restricting the papers to Congress participants, we asked the Ieading mathematicians in the field of the theory of reproducing kern eIs to submit papers. However, due to time restrietions and a compulsion to limit the Proceedings a reasonable size, we were unable to obtain a comprehensive treatment of the theory of reproducing kernels. Nevertheless, we hope this Proceedings of the First International Conference on reproducing kerneis will become a significant reference volume. Indeed, we believe that the theory of reproducing kernels will stand out as a fundamental and beautiful contribution in mathematical sciences with a broad array of applications to other areas of mathematics and science. We would like to thank Professor Robert Gilbert for his substantial contri bu tions to the Congress and to our Proceedings. We also express our sincere thanks to the staff of the University of Delaware for their manifold cooperation in organizing the Congress.

Author : Frank Nijhoff
Publisher : Springer Nature
ISBN 13 : 3030570002
Total Pages : 240 pages
Book Rating : 4.02/5 ( download)

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Download or read book Asymptotic, Algebraic and Geometric Aspects of Integrable Systems written by Frank Nijhoff and published by Springer Nature. This book was released on 2020-10-23 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume gathers together selected works from the 2018 “Asymptotic, Algebraic and Geometric Aspects of Integrable Systems” workshop that was held at TSIMF Yau Mathematical Sciences Center in Sanya, China, honoring Nalini Joshi on her 60th birthday. The papers cover recent advances in asymptotic, algebraic and geometric methods in the study of discrete integrable systems. The workshop brought together experts from fields such as asymptotic analysis, representation theory and geometry, creating a platform to exchange current methods, results and novel ideas. This volume's articles reflect these exchanges and can be of special interest to a diverse group of researchers and graduate students interested in learning about current results, new approaches and trends in mathematical physics, in particular those relevant to discrete integrable systems.

Author : Ciprian G Gal
Publisher : World Scientific
ISBN 13 : 9814590614
Total Pages : 204 pages
Book Rating : 4.17/5 ( download)

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Download or read book Evolution Equations with a Complex Spatial Variable written by Ciprian G Gal and published by World Scientific. This book was released on 2014-03-18 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates several classes of partial differential equations of real time variable and complex spatial variables, including the heat, Laplace, wave, telegraph, Burgers, Black–Merton–Scholes, Schrödinger and Korteweg–de Vries equations. The complexification of the spatial variable is done by two different methods. The first method is that of complexifying the spatial variable in the corresponding semigroups of operators. In this case, the solutions are studied within the context of the theory of semigroups of linear operators. It is also interesting to observe that these solutions preserve some geometric properties of the boundary function, like the univalence, starlikeness, convexity and spirallikeness. The second method is that of complexifying the spatial variable directly in the corresponding evolution equation from the real case. More precisely, the real spatial variable is replaced by a complex spatial variable in the corresponding evolution equation and then analytic and non-analytic solutions are sought. For the first time in the book literature, we aim to give a comprehensive study of the most important evolution equations of real time variable and complex spatial variables. In some cases, potential physical interpretations are presented. The generality of the methods used allows the study of evolution equations of spatial variables in general domains of the complex plane. Contents:Historical Background and MotivationHeat and Laplace Equations of Complex Spatial VariablesHigher-Order Heat and Laplace Equations with Complex Spatial VariablesWave and Telegraph Equations with Complex Spatial VariablesBurgers and Black–Merton–Scholes Equations with Complex Spatial VariablesSchrödinger-Type Equations with Complex Spatial VariablesLinearized Korteweg–de Vries Equations with Complex Spatial VariablesEvolution Equations with a Complex Spatial Variable in General Domains Readership: Graduates and researchers in partial differential equations and in classical analytical function theory of one complex variable. Key Features:For the first time in literature, the study of evolution equations of real time variable and complex spatial variables is madeThe study includes some of the most important classes of partial differential equations: heat, Laplace, wave, telegraph, Burgers, Black–Merton–Scholes, Schrodinger and Korteweg–de Vries equationsThe book is entirely based on the authors' own workKeywords:Evolution Equations of Complex Spatial Variables;Semigroup of Linear Operators;Complex Convolution Integrals;Heat;Laplace;Wave;Telegraph;Burgers;Black–Merton–Scholes;Schrodinger;Korteweg–de Vries Equations

Author : Luigi Rodino
Publisher : World Scientific
ISBN 13 : 9814543403
Total Pages : 332 pages
Book Rating : 4.08/5 ( download)

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Download or read book Partial Differential Equations And Their Applications - Proceedings Of The Conference written by Luigi Rodino and published by World Scientific. This book was released on 1999-11-26 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reports the recent progress in linear and nonlinear partial differential equations, microlocal analysis, singular partial differential operators, spectral analysis and hyperfunction theory.