Topic
Topological group
About: Topological group is a research topic. Over the lifetime, 3415 publications have been published within this topic receiving 54234 citations.
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Book•
01 Jan 1962
TL;DR: In this paper, the basic theorem of Fourier analysis on ordered groups has been studied, and the structure of locally compact Abelian groups has also been studied in the context of topology.
Abstract: The Basic Theorems of Fourier Analysis. The Structure of Locally Compact Abelian Groups. Idempotent Measures. Homomorphisms of Group Algebras. Measures and Fourier Transforms on Thin Sets. Functions of Fourier Transforms. Closed Ideals in L 1 (G). Fourier Analysis on Ordered Groups. Closed Subalgebras of L 1 (G). Appendices: Topology, Topological Groups, Banach Spaces, Banach Algebras, Measure Theory. Bibliography. List of Special Symbols. Index.
2,443 citations
TL;DR: In this paper, the authors present conditions générales d'utilisation (http://www.numdam.org/conditions), i.e., Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
Abstract: © Publications mathématiques de l’I.H.É.S., 1977, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
1,667 citations
Book•
01 Jan 1966
TL;DR: The history of the calculus can be traced back to the Calculus of Differential and Integral Calculus (DIC) as discussed by the authors, which is a generalization of the integral calculus.
Abstract: * General Introduction * Tools from Logic * Differential and Integral Calculus * General Topology * Functions of a Real Variable * Functions of a Complex Variable * Linear Spaces * Topological Groups and Lie Groups * Selected Topics * Concerning the History of the Calculus
1,386 citations
Book•
01 Jan 1963TL;DR: A brief review of some of the terminology and the elementary theorems of general topology, an examination of the new concept "linear topological space" in terms of more familiar notions, and a comparison of this new concept with the mathematical objects of which it is an abstraction can be found in this paper.
Abstract: This chapter is largely preliminary in nature; it consists of a brief review of some of the terminology and the elementary theorems of general topology, an examination of the new concept “linear topological space” in terms of more familiar notions, and a comparison of this new concept with the mathematical objects of which it is an abstraction. After an introductory section on topology, we consider linear topological spaces, subspaces, quotient spaces, product spaces, and linear functions. With the exception of a few simple propositions relating to circled sets, these theorems are specializations of familiar results on topological groups (in other words, little use is made of scalar multiplication).
836 citations