Linear Differential Equations in the Complex Domain

From Classical Theory to Forefront

Yoshishige Haraoka (Autor)

Buch | Softcover

XIII, 396 Seiten

2020 | 1st ed. 2020
Springer International Publishing (Verlag)
978-3-030-54662-5 (ISBN)

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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 usedifferential equations.

- Introduction. - Part I Ordinary Differential Equations. - Scalar Differential Equations and Systems of Differential Equations. - Analysis at a Regular Point. - Regular Singular Points. - Monodromy. - Connection Problem. - Fuchsian Differential Equations. - Deformation Theory. - Integral Representations of Solutions of Euler Type. - Irregular Singular Points. - Part II Completely Integrable Systems. - Linear Pfaffian Systems and Integrability Condition. - Regular Singularity. - Monodromy Representations. - Middle Convolution.

"The author has made many contributions to the related global theory of Fuchsian equations, including hypergeometric-type equations and Okubo systems. In this monograph, the author leads the reader to the forefront of this field." (Shun Shimomura, Mathematical Reviews, March, 2022)

"The main purpose of this interesting book is an introduction to recent developments in the theory of linear ordinary differential systems and linear completely integrable total differential systems. ... The book is designed to be suitable for use as a primary textbook in an advanced graduate course or as a supplementary source for beginning graduate courses. ... The book contains numerous examples, which can be useful as a reference for researchers." (Valentine Tyshchenko, zbMATH 1460.34002, 2021)

Erscheinungsdatum	18.11.2020
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XIII, 396 p. 47 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	629 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Differential Equations • Integrable Systems • middle convolution • Monodromy • rigidity
ISBN-10	3-030-54662-4 / 3030546624
ISBN-13	978-3-030-54662-5 / 9783030546625
Zustand	Neuware