Asymptotic Analysis for Integrable Connections with Irregular Singular Points PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Asymptotic Analysis for Integrable Connections with Irregular Singular Points PDF full book. Access full book title Asymptotic Analysis for Integrable Connections with Irregular Singular Points by H. Majima. Download full books in PDF and EPUB format.
Author: H. Majima Publisher: Springer ISBN: 3540389318 Category : Mathematics Languages : en Pages : 169
Book Description
Using strongly asymptotic expansions of functions of several variables, we prove existence theorems of asymptotic solutions to integrable systems of partial differential equations of the first order with irregular singular points under certain general conditions. We also prove analytic splitting lemmas for completely integrable linear Pfaffian systems. Moreover, for integrable connections with irregular singular points, we formulate and solve the Riemann-Hilbert-Birkhoff problem, and prove analogues of Poincare's lemma and de Rham cohomology theorem under certain general conditions.
Author: H. Majima Publisher: Springer ISBN: 3540389318 Category : Mathematics Languages : en Pages : 169
Book Description
Using strongly asymptotic expansions of functions of several variables, we prove existence theorems of asymptotic solutions to integrable systems of partial differential equations of the first order with irregular singular points under certain general conditions. We also prove analytic splitting lemmas for completely integrable linear Pfaffian systems. Moreover, for integrable connections with irregular singular points, we formulate and solve the Riemann-Hilbert-Birkhoff problem, and prove analogues of Poincare's lemma and de Rham cohomology theorem under certain general conditions.
Author: Yoshishige Haraoka Publisher: Springer Nature ISBN: 3030546632 Category : Mathematics Languages : en Pages : 396
Book Description
This book provides a detailed introduction to recent developments in the theory of linear differential systems and integrable total differential systems. Starting from the basic theory of linear ordinary differential equations and integrable systems, it proceeds to describe Katz theory and its applications, extending it to the case of several variables. In addition, connection problems, deformation theory, and the theory of integral representations are comprehensively covered. Complete proofs are given, offering the reader a precise account of the classical and modern theory of linear differential equations in the complex domain, including an exposition of Pfaffian systems and their monodromy problems. The prerequisites are a course in complex analysis and the basics of differential equations, topology and differential geometry. This book will be useful for graduate students, specialists in differential equations, and for non-specialists who want to use differential equations.
Author: Masaki Kashiwara Publisher: Springer Science & Business Media ISBN: 4431681701 Category : Mathematics Languages : en Pages : 324
Book Description
The 1990 Hayashibara Forum, "the International Conference on Special Functions", was held at Fujisaki Institute, Hayashibara Biochemical Laboratories, Inc., Okayama, Japan for five days (August 16-20, 1990). This volume is the proceedings for that meeting. On January 14,1985, Heisuke Hironaka and Ken Hayashibara, the president of Chair man, Board of Trustees, Hayashibara Foundation, met and decided to have an international conference on mathematics in the summer of 1990. This was pushed forward by Kiyosi Ito, who proposed "Special functions" as the theme of the conference. He also asked the present editors to join in the organizing committee of the Hayashibara Forum, 1990. On May 13, 1989 the organizing committee sent letters to major Japanese mathemat ical institutions asking their members to give suggestions about whom it should invite. Receiving the replies, the organizing committee decided the invited speakers, and sent invitation letters to them, in which it was written that "Special functions have been created and explored to describe scientific and mathematical phenomena. Trigonometric functions give the relation of angle to length. Riemann's zeta function was invented in order to describe the prime number distribution. Legendre's spherical functions and Bessel's functions were born in connection with the eigenvalue problems for partial differential equations.
Author: Marius van der Put Publisher: Springer Science & Business Media ISBN: 3642557503 Category : Mathematics Languages : en Pages : 446
Book Description
From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews
Author: Takahiro Kawai Publisher: World Scientific ISBN: 9814549045 Category : Languages : en Pages : 526
Book Description
A collection of papers on current topics and future problems in the theory of differential equations which were reported at the Taniguchi symposium (Katata) and RIMS symposium (Kyoto); Painlevé transcendents, Borel resummation, linear differential equations of infinite order, solvability of microdifferential equations, Gevrey index, etc. are among them.
Author: Michael Ruzhansky Publisher: John Wiley & Sons ISBN: 1119414334 Category : Mathematics Languages : en Pages : 1021
Book Description
An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.
Author: B L J Braaksma Publisher: World Scientific ISBN: 9814548081 Category : Languages : en Pages : 342
Book Description
The 16th Problem of Hilbert is one of the most famous remaining unsolved problems of mathematics. It concerns whether a polynomial vector field on the plane has a finite number of limit cycles. There is a strong connection with divergent solutions of differential equations, where a central role is played by the Stokes Phenomenon, the change in asymptotic behaviour of the solutions in different sectors of the complex plane.The contributions to these proceedings survey both of these themes, including historical and modern theoretical points of view. Topics covered include the Riemann-Hilbert problem, Painleve equations, nonlinear Stokes phenomena, and the inverse Galois problem.
Author: Yasutaka Sibuya Publisher: American Mathematical Soc. ISBN: 0821846760 Category : Mathematics Languages : en Pages : 286
Book Description
This book is a translation of a 1976 book originally written in Japanese. The main attention is paid to intrinsic aspects of problems related to linear ordinary differential equations in complex domains. Examples of the problems discussed in the book include the Riemann problem on the Riemann sphere, a characterization of regular singularities, and a classification of meromorphic differential equations. Since the original book was published, many new ideas have developed, such as applications of D-modules, Gevrey asymptotics, cohomological methods, $k$-summability, and studies of differential equations containing parameters. Five appendices, added in the present edition, briefly cover these new ideas. In addition, more than 100 references have been added. This book introduces the reader to the essential facts concerning the structure of solutions of linear differential equations in the complex domain and illuminates the intrinsic meaning of older results by means of more modern ideas. A useful reference for research mathematicians, this book would also be suitable as a textbook in a graduate course or seminar.
Author: H. Majima
Author: H. Majima
Author: Hideyuki Majima
Author: Edward William Stredulinsky
Author: Yoshishige Haraoka
Author: Masaki Kashiwara
Author: Marius van der Put
Author: Takahiro Kawai
Author: Michael Ruzhansky
Author: B L J Braaksma
Author: Yasutaka Sibuya