Postmodern Analysis
Publication year: 2005
ISBN: 978-3-540-28890-9
Internet Resource: Please Login to download book
“Modern Analysis” as represented in the works of the Bourbaki group or in the textbooks by Jean Dieudonn´ e is characterized by its systematic and axiomatic treatment and by its drive towards a high level of abstraction. Given the tendency of many prior treatises on analysis to degenerate into a collection of rather unconnected tricks to solve special problems, this de?nitely represented a healthy achievement. In any case, for the development of a consistent and powerful mathematical theory, it seems to be necessary to concentrate solely on the internal problems and structures and to neglect the relations to other ?elds of scienti?c, even of mathematical study for a certain while. Almost complete isolation may be required to reach the level of intellectual elegance and perfection that only a good mathem- ical theory can acquire. However, once this level has been reached, it can be useful to open one’s eyes again to the inspiration coming from concrete external problems.
Subject: Mathematics and Statistics, Banach and Hilbert space, Continuous and differentiable functions, Lebesgue integration theory, Sobolev space, Sobolov spaces, analysis, calculus of variations, differential equations, implicit function theorem
