Représentation régulière

Résumé

En mathématiques et plus précisément en théorie des groupes, les représentations régulières (gauche et droite) d'un groupe G sont les représentations de G associées aux deux actions (à gauche et à droite) de G sur lui-même par translation. Si G est un groupe fini ce sont, pour un corps fixé K, deux actions linéaires de G sur le K-espace vectoriel KG des applications de G dans K. Si G est un groupe localement compact, ce sont deux représentations continues unitaires de G sur un certain espace de Hilbert inclus dans ℂG. Définition Représentation de groupe

Sur le K-espace vectoriel KG des applications de G dans K, la représentation régulière gauche de G, notée λ, est donnée par\forall g,h\in G,\quad\forall f\in K^G,\qquad\lambda_g(f)(h)=f(g^{-1}h)et la droite, notée ρ, par \forall g,h\in G,\quad\forall f\in K^G,\qquad\rho_g(f)(h)=f(hg).
En particulier les fonctions δk pour k∊G, qui sont définies par\forall h\in G,\qquad\delta_k(h)=\begin{ca

Source officielle

https://fr.wikipedia.org/wiki/Repr%C3%A9sentation_r%C3%A9guli%C3%A8re

À propos de ce résultat

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Publications associées (2)

Publications associées

Chargement

Personnes associées

Chargement

Unités associées

Aucun résultat

Unités associées

Chargement

Concepts associés (24)

Concepts associés

Chargement

Cours associés (3)

Study the basics of representation theory of groups and associative algebras.

The aim of the course is to give an introduction to linear algebraic groups and to give an insight into a beautiful subject that combines algebraic geometry with group theory.

Participants of this course will master computational techniques frequently used in mathematical finance applications. Emphasis will be put on the implementation and practical aspects.

Cours associés

Chargement

Séances de cours associées (10)

Séances de cours associées

Chargement

Cramer-Karhunen-Loeve representation and harmonic principal component analysis of functional time series

Victor Panaretos, Shahin Tavakoli

We develop a doubly spectral representation of a stationary functional time series, and study the properties of its empirical version. The representation decomposes the time series into an integral of uncorrelated frequency components (Cramer representation), each of which is in turn expanded in a Karhunen-Loeve series. The construction is based on the spectral density operator, the functional analogue of the spectral density matrix, whose eigenvalues and eigenfunctions at different frequencies provide the building blocks of the representation. By truncating the representation at a finite level, we obtain a harmonic principal component analysis of the time series, an optimal finite dimensional reduction of the time series that captures both the temporal dynamics of the process, as well as the within-curve dynamics. Empirical versions of the decompositions are introduced, and a rigorous analysis of their large-sample behaviour is provided, that does not require any prior structural assumptions such as linearity or Gaussianity of the functional time series, but rather hinges on Brillinger-type mixing conditions involving cumulants. (c) 2013 Elsevier B.V. All rights reserved.

Elsevier2013

Chargement

Protection of data from erasures using subsymbol based codes

Mohammad Amin Shokrollahi

An encoder uses output symbol subsymbols to effect or control a tradeoff of computational effort and overhead efficiency to, for example, greatly reduce computational effort for the cost of a small amount of overhead efficiency. An encoder reads an ordered plurality of input symbols, comprising an input file or input stream, and produces output subsymbol. The ordered plurality of input symbols are each selected from an input alphabet, and the generated output subsymbols comprise selections among an output subsymbol alphabet. An output subsymbol is generated using a function evaluator applied to subsymbols of the input symbols. The encoder may be called one or more times, each time producing an output subsymbol. Output subsymbols can then be assembled into output symbols and transmitted to their destination. The functions used to generate the output subsymbols from the input subsymbols can be XOR's of some of the input subsymbols and these functions are obtained from a linear code defined over an extension field of GF(2) by transforming each entry in a generator or parity-check matrix of this code into an appropriate binary matrix using a regular representation of the extension field over GF(2). In a decoder, output subsymbols received by the recipient are obtained from output symbols transmitted from one sender that generated those output symbols based on an encoding of an input sequence (file, stream, etc.).

2008

Chargement