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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Ten mathematical essays on approximation in analysis and topology. Amsterdam ; Oxford : Elsevier, 2005 (OCoLC)58556141 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
J Ferrera; Julián López-Gómez; F R Ruiz del Portal |

ISBN: | 9780444518613 0444518614 0080459196 9780080459196 1280634049 9781280634048 |

OCLC Number: | 162130287 |

Description: | 1 online resource (xii, 270 pages) |

Contents: | Maximum principles and principal eigenvalues (H. Amann). -- On some approximation problems in topology (A.N. Dranishnikov). -- Eigenvalues and perturbed domains (J.K. Hale). -- Monotone approximations and rapid convergence (V. Lakshmikantham). -- Spectral theory and nonlinear analysis (J. L̤pez-G̤mez). -- Approximating topological spaces by polyhedra (S. Mardesic). -- Periodic solutions in the golden sixties: the birth of a continuation theorem (J. Mawhin). -- The stability of the equilibrium: a search for the right approximation (R. Ortega). -- The Bishop--Phelps theorem (R.R. Phelps). -- An essay on some problems of approximation theory (A.G. Ramm). |

Responsibility: | edited by J. Ferrera, J. López-Gómez, F.R. Ruiz del Portal. |

### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

This book collects 10 mathematical essays on approximation in Analysis and Topology by some of the most influent mathematicians of the last third of the 20th Century. Besides the papers contain the very ultimate results in each of their respective fields, many of them also include a series of historical remarks about the state of mathematics at the time they found their most celebrated results, as well as some of their personal circumstances originating them, which makes particularly attractive the book for all scientist interested in these fields, from beginners to experts. These gem pieces of mathematical intra-history should delight to many forthcoming generations of mathematicians, who will enjoy some of the most fruitful mathematics of the last third of 20th century presented by their own authors. The contains cover a wide range of new mathematical results. Among them, the most advanced characterisations of very weak versions of the classical maximum principle, the very last results on global bifurcation theory, algebraic multiplicities, general dependencies of solutions of boundary value problems with respect to variations of the underlying domains, the deepest available results in rapid monotone schemes applied to the resolution of non-linear boundary value problems, the intra-history of the the genesis of the first general global continuation results in the context of periodic solutions of nonlinear periodic systems, as well as the genesis of the coincidence degree, some novel applications of the topological degree for ascertaining the stability of the periodic solutions of some classical families of periodic second order equations, the resolution of a number of conjectures related to some very celebrated approximation problems in topology and inverse problems, as well as a number of applications to engineering, an extremely sharp discussion of the problem of approximating topological spaces by polyhedra using various techniques based on inverse systems, as well as homotopy expansions, and the Bishop-Phelps theorem. Read more...

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