Search results for "BERT"

Los pasados políticos de Grass / Ridruejo

2006

Partial $\ast$-algebras of distributions

2005

The problem of multiplying elements of the conjugate dual of certain kind of commutative generalized Hilbert algebras, which are dense in the set of C ∞ -vectors of a self-adjoint operator, is considered in the framework of the so-called duality method. The multiplication is defined by identifying each distribution with a multiplication operator acting on the natural rigged Hilbert space. Certain spaces, that are an

Beyond frames: Semi-frames and reproducing pairs

2017

Frames are nowadays a standard tool in many areas of mathematics, physics, and engineering. However, there are situations where it is difficult, even impossible, to design an appropriate frame. Thus there is room for generalizations, obtained by relaxing the constraints. A first case is that of semi-frames, in which one frame bound only is satisfied. Accordingly, one has to distinguish between upper and lower semi-frames. We will summarize this construction. Even more, one may get rid of both bounds, but then one needs two basic functions and one is led to the notion of reproducing pair. It turns out that every reproducing pair generates two Hilbert spaces, conjugate dual of each other. We …

PIP-Spaces and Signal Processing

2009

Contemporary signal processing makes an extensive use of function spaces, always with the aim of getting a precise control on smoothness and decay properties of functions. In this chapter, we will discuss several classes of such function spaces that have found interesting applications, namely, mixed-norm spaces, amalgam spaces, modulation spaces, or Besov spaces. It turns out that all those spaces come in families indexed by one or more parameters, that specify, for instance, the local behavior or the asymptotic properties. In general, a single space, taken alone, does not have an intrinsic meaning, it is the family as a whole that does, which brings us to the very topic of this volume. In …

Tensor product characterizations of mixed intersections of non quasianalytic classes and kernel theorems

2009

Mixed intersections of non quasi-analytic classes have been studied in [12]. Here we obtain tensor product representations of these spaces that lead to kernel theorems as well as to tensor product representations of intersections of non quasi-analytic classes on product of open or of compact sets (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Examples of Indexed PIP-Spaces

2009

This chapter is devoted to a detailed analysis of various concrete examples of pip-spaces. We will explore sequence spaces, spaces of measurable functions, and spaces of analytic functions. Some cases have already been presented in Chapters 1 and 2. We will of course not repeat these discussions, except very briefly. In addition, various functional spaces are of great interest in signal processing (amalgam spaces, modulation spaces, Besov spaces, coorbit spaces). These will be studied systematically in a separate chapter (Chapter 8).

Invertibility in tensor products of Q-algebras

2002

Spectrum and Pseudo-Spectrum

2019

In this book all Hilbert spaces will be assumed to separable for simplicity. In this section we review some basic definitions and properties; we refer to Kato (Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132. Springer, New York, 1966), Reed and Simon (Methods of modern mathematical physics. I. Functional analysis, 2nd edn. Academic, New York, 1980; Methods of modern mathematical physics. II. Fourier analysis, self adjointness. Academic, New York, 1975; Methods of modern mathematical physics. IV. Analysis of operators. Academic, New York, 1978), Riesz and Sz.-Nagy (Lecons d’analyse fonctionnelle, Quatrieme edition. Academie des Sciences d…

Current Algebras as Hilbert Space Operator Cocycles

1994

Aspects of a generalized representation theory of current algebras in 3 + 1 dimensions axe discussed. Rules for a systematic computation of vacuum expectation values of products of currents are described. Their relation to gauge group actions in bundles of fermionic Fock spaces and to the sesquilinear form approach of Langmann and Ruijsenaars is explained. The regularization for a construction of an operator cocycle representation of the current algebra is explained. An alternative formula for the Schwinger terms defining gauge group extensions is written in terms of Wodzicki residue and Dixmier trace.

À bas les chefs ! : écrits libertaires (1847-1863)

2016

International audience; Ce livre n’est point écrit avec de l’encre, c’est de l’acier tourné en in-8° et chargé de fulminate d’idées. C’est un projectile autoricide que je jette à mille exemplaires sur le pavé des civilisés. » Toute sa vie, balloté par la misère et l’exil, Déjacque n’a cessé d’écrire. Ouvrier colleur de son état, « poète des misérables », comme le surnomme son ami Gustave Lefrançais, « tapageur acharné », il s’arme de sa plume contre les réactionnaires de tout poil. En 1848 à Paris, il chante la gloire des insurgés de Juin, ce qui lui vaut la condamnation et l’exil. À Londres, puis Jersey, où il côtoie les proscrits, il s’attire les foudres des républicains dont il fustige l…