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I.M.Gelfand, one of the leading contemporary mathematicians,
largely determined the modern view of functional analysis with its
numerous relations to other branches of mathematics, including
mathematical physics, algebra, topology, differential geometry and
analysis. With the publication of these Collected Papers in three
volumes Gelfand gives a representative choice of his papers written
in the last fifty years. Gelfand's research led to the development
of remarkable mathematical theories - most now classics - in the
field of Banach algebras, infinite-dimensional representations of
Lie groups, the inverse Sturm-Liouville problem, cohomology of
infinite-dimensional Lie algebras, integral geometry, generalized
functions and general hypergeometric functions. The corresponding
papers form the major part of the Collected Papers. Some articles
on numerical methods and cybernetics as well as a few on biology
are included. A substantial part of the papers have been translated
into English especially for this edition. This edition is rounded
off by a preface by S.G.Gindikin, a contribution by V.I.Arnold and
an extensive bibliography with almost 500 references. Gelfand's
Collected Papers will provide stimulating and serendipitous reading
for researchers in a multitude of mathematical disciplines.
Equivariant cohomology on smooth manifolds is the subject of this
book which is part of a collection of volumes edited by J. Bruning
and V.W. Guillemin. The point of departure are two relatively short
but very remarkable papers be Henry Cartan, published in 1950 in
the Proceedings of the "Colloque de Topologie." These papers are
reproduced here, together with a modern introduction to the
subject, written by two of the leading experts in the field. This
"introduction" comes as a textbook of its own, though, presenting
the first full treatment of equivariant cohomology in the de Rahm
setting. The well known topological approach is linked with the
differential form aspect through the equivariant de Rahm theorem.
The systematic use of supersymmetry simplifies considerably the
ensuing development of the basic technical tools which are then
applied to a variety of subjects, leading up to the localization
theorems and other very recent results."
What is the true mark of inspiration? Ideally it may mean the
originality, freshness and enthusiasm of a new breakthrough in
mathematical thought. The reader will feel this inspiration in all
four seminal papers by Duistermaat, Guillemin and H rmander
presented here for the first time ever in one volume. However, as
time goes by, the price researchers have to pay is to sacrifice
simplicity for the sake of a higher degree of abstraction. Thus the
original idea will only be a foundation on which more and more
abstract theories are being built. It is the unique feature of this
book to combine the basic motivations and ideas of the early
sources with knowledgeable and lucid expositions on the present
state of Fourier Integral Operators, thus bridging the gap between
the past and present. A handy and useful introduction that will
serve novices in this field and working mathematicians equally
well.
Equivariant cohomology on smooth manifolds is the subject of this
book which is part of a collection of volumes edited by J. Bruning
and V.W. Guillemin. The point of departure are two relatively short
but very remarkable papers be Henry Cartan, published in 1950 in
the Proceedings of the "Colloque de Topologie." These papers are
reproduced here, together with a modern introduction to the
subject, written by two of the leading experts in the field. This
"introduction" comes as a textbook of its own, though, presenting
the first full treatment of equivariant cohomology in the de Rahm
setting. The well known topological approach is linked with the
differential form aspect through the equivariant de Rahm theorem.
The systematic use of supersymmetry simplifies considerably the
ensuing development of the basic technical tools which are then
applied to a variety of subjects, leading up to the localization
theorems and other very recent results."
What is the true mark of inspiration? Ideally it may mean the
originality, freshness and enthusiasm of a new breakthrough in
mathematical thought. The reader will feel this inspiration in all
four seminal papers by Duistermaat, Guillemin and H rmander
presented here for the first time ever in one volume. However, as
time goes by, the price researchers have to pay is to sacrifice
simplicity for the sake of a higher degree of abstraction. Thus the
original idea will only be a foundation on which more and more
abstract theories are being built. It is the unique feature of this
book to combine the basic motivations and ideas of the early
sources with knowledgeable and lucid expositions on the present
state of Fourier Integral Operators, thus bridging the gap between
the past and present. A handy and useful introduction that will
serve novices in this field and working mathematicians equally
well.
I.M. Gelfand (1913 - 2009), one of the world's leading contemporary
mathematicians, largely determined the modern view of functional
analysis with its numerous relations to other branches of
mathematics, including mathematical physics, algebra, topology,
differential geometry and analysis. In this three-volume Collected
Papers Gelfand presents a representative sample of his work.
Gelfand's research led to the development of remarkable
mathematical theories - most of which are now classics - in the
field of Banach algebras, infinite-dimensional representations of
Lie groups, the inverse Sturm-Liouville problem, cohomology of
infinite-dimensional Lie algebras, integral geometry, generalized
functions and general hypergeometric functions. The corresponding
papers form the major part of the collection. Some articles on
numerical methods and cybernetics as well as a few on biology are
also included. A substantial number of the papers have been
translated into English especially for this edition. The collection
is rounded off by an extensive bibliography with almost 500
references. Gelfand's Collected Papers will be a great stimulus,
especially for the younger generation, and will provide a strong
incentive to researchers.
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