Download E-books Linear Differential Equations in the Complex Domain: Problems of Analytic Continuation (Translations of Mathematical Monographs) PDF

By Yasutaka Sibuya

Study in differential equations is mostly orientated towards particular effects and influenced through functions. Many smart tools were found during this means, yet, whilst difficulties of extra primary hassle come up, researchers needs to locate whatever intrinsic within the arithmetic itself for you to make growth. As examine in topology, algebraic geometry, and features of a number of advanced variables have complicated, many equipment helpful in such fields have been brought into the research of differential equations. the most a part of this publication is a translation of a 1976 ebook initially written in jap. The booklet, focusing realization on intrinsic points of the topic, explores a few difficulties of linear usual differential equations in advanced domain names. Examples of the issues mentioned comprise the Riemann challenge at the Riemann sphere, a characterization of standard singularities, and a class of meromorphic differential equations. because the unique e-book was once released, many new principles have constructed, reminiscent of purposes of D-modules, Gevrey asymptotics, cohomological equipment, $k$-summability, and reviews of differential equations containing parameters. 5 appendices, additional within the current variation, in short conceal those new rules. moreover, greater than a hundred references were extra. This publication will introduce readers to the basic evidence about the constitution of options of linear differential equations within the advanced area, in addition to light up the intrinsic that means of older effects by way of extra smooth principles. an invaluable reference for examine mathematicians on numerous primary effects, this e-book may even be appropriate as a textbook in a graduate path or seminar.