Introduction to Various Aspects of Degree Theory in Banach Spaces is popular PDF and ePub book, written by E. H. Rothe in 1986-12-31, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Introduction to Various Aspects of Degree Theory in Banach Spaces can be Read Online from any device for your convenience.
Introduction to Various Aspects of Degree Theory in Banach Spaces Book PDF Summary
Since its development by Leray and Schauder in the 1930's, degree theory in Banach spaces has proved to be an important tool in tackling many analytic problems, including boundary value problems in ordinary and partial differential equations, integral equations, and eigenvalue and bifurcation problems. With this volume E. H. Rothe provides a largely self-contained introduction to topological degree theory, with an emphasis on its function-analytical aspects. He develops the definition and properties of the degree as much as possible directly in Banach space, without recourse to finite-dimensional theory. A basic tool used is a homotopy theorem for certain linear maps in Banach spaces which allows one to generalize the distinction between maps with positive determinant and those with negative determinant in finite-dimensional spaces. Rothe's book is addressed to graduate students who may have only a rudimentary knowledge of Banach space theory. The first chapter on function-analytic preliminaries provides most of the necessary background. For the benefit of less experienced mathematicians, Rothe introduces the topological tools (subdivision and simplicial approximation, for example) only to the degree of abstraction necessary for the purpose at hand. Readers will gain insight into the various aspects of degree theory, experience in function-analytic thinking, and a theoretic base for applying degree theory to analysis. Rothe describes the various approaches that have historically been taken towards degree theory, making the relationships between these approaches clear. He treats the differential method, the simplicial approach introduced by Brouwer in 1911, the Leray-Schauder method (which assumes Brouwer's degree theory for the finite-dimensional space and then uses a limit process in the dimension), and attempts to establish degree theory in Banach spaces intrinsically, by an application of the differential method in the Banach space case.
Detail Book of Introduction to Various Aspects of Degree Theory in Banach Spaces PDF
- Author : E. H. Rothe
- Release : 31 December 1986
- Publisher : American Mathematical Soc.
- ISBN : 9780821827703
- Genre : Mathematics
- Total Page : 250 pages
- Language : English
- PDF File Size : 8,9 Mb
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