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Théories Spectrales: Chapitres 1 Et 2
Paperback
ISBN13: 9783030140632
Publisher: Springer Nature
Published: Jul 30 2019
Pages: 336
Weight: 1.09
Height: 0.73 Width: 6.14 Depth: 9.21
Language: French
Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements.
Le Livre de Théories spectrales est consacré à l'étude des algèbres normées et de leurs applications. Le premier chapitre met en place la théorie fondamentale des algèbres de Banach et des algèbres stellaires. Nous y présentons l'équivalence de catégories entre algèbres stellaires commutatives et espaces topologiques localement compacts, ainsi que le calcul fonctionnel holomorphe en plusieurs variables dans une algèbre de Banach commutative.
La transformation de Fourier, qui est l'un des outils mathématiques les plus universels, est étudiée au second chapitre, dans le cadre des groupes localement compacts commutatifs.
Le texte est complété par de nombreux exercices.
Ces deux chapitres forment une édition entièrement refondue de l'édition de 1967.
The Elements of Mathematics of Nicolas Bourbaki have the goal of giving a rigorous and systematic presentation of mathematics starting from the foundations, without prerequisites. The book of Spectral Theories is devoted to the study of normed algebras and their applications. The first chapter establishes the basic theory of Banach algebras and C*-algebras. We present the equivalence of categories between commutative C*-algebras and locally compact topological spaces, as well as the holomorphic functional calculus in several variables in a commutative Banach algebra.
The Fourier transform, which is one of the most universal mathematical tools, is studied in the second chapter, in the context of locally compact commutative topological groups.The text is accompanied by many exercices.
These two chapters are completely updated new versions of the 1967 original edition.
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