Analytic Sets In Locally Convex Spaces (mathematics Studies)
by Pierre Mazet /
1984 / English / PDF
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The theory of analytic functions has been generalized to a large
extent to spaces of infinite dimension. This volume has uncovered
many new directions of interest, and certain phenomena whose deeper
investigation has led to a better knowledge of the theory,
including the finite dimensional case.[...] This work is placed in
the framework of locally convex spaces, which is necessary in
particular for the study of problems relating to spectra.
The theory of analytic functions has been generalized to a large
extent to spaces of infinite dimension. This volume has uncovered
many new directions of interest, and certain phenomena whose deeper
investigation has led to a better knowledge of the theory,
including the finite dimensional case.[...] This work is placed in
the framework of locally convex spaces, which is necessary in
particular for the study of problems relating to spectra.
The present work comes in three parts. The first part generalizes
several techniques of Commutative Algebra to the non-Noetherian
situations which are met in the study of infinite dimensional
spaces. The second part, which is the most important, is dedicated
to the geometrical study itself. In this section the author
generalizes the theorems on the local representation of analytic
spaces and the great classical theorems: the Nullstellensatz, the
Direct Image theorem and the theorem of Remmert-Stein. The third
part contains three appendices which cover several open problems,
as well as other aspects of the theory of analytic functions.
The present work comes in three parts. The first part generalizes
several techniques of Commutative Algebra to the non-Noetherian
situations which are met in the study of infinite dimensional
spaces. The second part, which is the most important, is dedicated
to the geometrical study itself. In this section the author
generalizes the theorems on the local representation of analytic
spaces and the great classical theorems: the Nullstellensatz, the
Direct Image theorem and the theorem of Remmert-Stein. The third
part contains three appendices which cover several open problems,
as well as other aspects of the theory of analytic functions.
