Multidimensional Residues and Their Applications
Author | : A. K. T͡Sikh |
Publisher | : American Mathematical Soc. |
Total Pages | : 187 |
Release | : 1992 |
ISBN-10 | : 0821845608 |
ISBN-13 | : 9780821845608 |
Rating | : 4/5 (608 Downloads) |
Download or read book Multidimensional Residues and Their Applications written by A. K. T͡Sikh and published by American Mathematical Soc.. This book was released on 1992 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: The technique of residues is known for its many applications in different branches of mathematics. Tsikh's book presents a systematic account of residues associated with holomorphic mappings and indicates many applications. The book begins with preliminaries from the theory of analytic sets, together with material from algebraic topology that is necessary for the integration of differential forms over chains. Tsikh then presents a detailed study of residues associated with mappings that preserve dimension (local residues). Local residues are applied to algebraic geometry and to problems connected with the investigation and calculation of double series and integrals. There is also a treatment of residues associated with mappings that reduce dimension - that is, residues of semimeromorphic forms, connected with integration over tubes around nondiscrete analytic sets.