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.
This book covers 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.
Key features:
- It contains a number of seminal contributions by some of the most
world leading mathematicians of the second half of the 20th
Century.
- The papers cover a complete range of topics, from the
intra-history of the involved mathematics to the very last
developments in Differential Equations, Inverse Problems, Analysis,
Nonlinear Analysis and Topology.
- All contributed papers are self-contained works containing rather
complete list of references on each of the subjects covered.
- The book contains some of the very last findings concerning the
maximum principle, the theory of monotone schemes in nonlinear
problems, the theory of algebraic multiplicities, global
bifurcation theory, dynamics of periodic equations and systems,
inverse problems and approximation in topology.
- The papers are extremely well written and directed to a wide
audience, from beginners to experts. An excellent occasion to
become engaged with some of the most fruitful mathematics developed
during the last decades.
. It contains a number of seminal contributions by some of the most
world leading mathematicians of the second half of the 20th
Century.
. The papers cover a complete range of topics, from the
intra-history of the involved mathematics to the very last
developments in Differential Equations, Inverse Problems, Analysis,
Nonlinear Analysis and Topology.
. All contributed papers are self-contained works containing rather
complete list of references on each of the subjects covered.
. The book contains some of the very last findings concerning the
maximum principle, the theory of monotone schemes in nonlinear
problems, the theory of algebraic multiplicities, global
bifurcation theory, dynamics of periodic equations and systems,
inverse problems and approximation in topology.
. The papers are extremely well written and directed to a wide
audience, from beginners to experts. An excellent occasion to
become engaged with some of the most fruitful mathematics developed
during the last decades."
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