| History of Functional Analysis: Volume 49 Contributor(s): Dieudonne, J. (Author) |
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ISBN: 0444861483 ISBN-13: 9780444861481 Publisher: North-Holland OUR PRICE: $207.90 Product Type: Hardcover - Other Formats Published: January 1983 |
| Additional Information |
| BISAC Categories: - Mathematics | Calculus - Mathematics | History & Philosophy - Mathematics | Functional Analysis |
| Dewey: 515.709 |
| LCCN: 80028960 |
| Series: North-Holland Mathematics Studies |
| Physical Information: 0.75" H x 7" W x 10" (1.70 lbs) 320 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: History of Functional Analysis presents functional analysis as a rather complex blend of algebra and topology, with its evolution influenced by the development of these two branches of mathematics. The book adopts a narrower definition--one that is assumed to satisfy various algebraic and topological conditions. A moment of reflections shows that this already covers a large part of modern analysis, in particular, the theory of partial differential equations. This volume comprises nine chapters, the first of which focuses on linear differential equations and the Sturm-Liouville problem. The succeeding chapters go on to discuss the crypto-integral equations, including the Dirichlet principle and the Beer-Neumann method; the equation of vibrating membranes, including the contributions of Poincare and H.A. Schwarz's 1885 paper; and the idea of infinite dimension. Other chapters cover the crucial years and the definition of Hilbert space, including Fredholm's discovery and the contributions of Hilbert; duality and the definition of normed spaces, including the Hahn-Banach theorem and the method of the gliding hump and Baire category; spectral theory after 1900, including the theories and works of F. Riesz, Hilbert, von Neumann, Weyl, and Carleman; locally convex spaces and the theory of distributions; and applications of functional analysis to differential and partial differential equations. This book will be of interest to practitioners in the fields of mathematics and statistics. |