منابع مشابه
Some Facets of an Lca Group inside Its Bohr Compactification
Let be a non-discrete LCA (locally compact abelian) group, its dual. ( ) ∧, where denotes discrete, is the Bohr compactification of , denoted by . There exists a continuous group isomorphism ί: → of onto a proper dense subgroup of . This subgroup to be denoted by ί is the main object of our study. A subgroup of is pure if ∩ = for each positive integer . We define to be strongly pure if is pure ...
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We study a class of generalized Riesz products connected to the spectral type of some class of rank one flows on R. Applying a Central Limit Theorem of Kac, we exhibit a large class of singular generalized Riesz products on the Bohr compactification of R. Moreover, we discuss the problem of the flat polynomials in this setting. Dedicated to Professors Jean-Paul Thouvenot and Bernard Host. AMS S...
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In quantum physics, the value of an observable such as the position or velocity of a particle can generally only be predicted statistically, by the probability of finding a particular value. Niels Bohr, one of the founders of quantum mechanics, considered the probabilistic nature of the predictions of this theory to be fundamental. However, for Albert Einstein, the impossibility of predicting t...
متن کاملThe concept of boundedness and the Bohr compactification of a MAP Abelian group
Let G be a maximally almost periodic (MAP) Abelian group and let B be a boundedness on G in the sense of Vilenkin. We study the relations between B and the Bohr topology of G for some well known groups with boundedness (G,B). As an application, we prove that the Bohr topology of a topological group which is topologically isomorphic to the direct product of a locally convex space and an L∞-group...
متن کاملQuantum monodromy and Bohr-Sommerfeld rules
This article is based on a talk given in Dijon for the 2000 summer school “Topological and Geometrical Methods: Applications to Dynamical Systems”. The standard definitions of the monodromy invariant for completely integrable classical systems are reviewed, and the link to the quantum monodromy observed in the joint spectrum of commuting operators is explained. The mathematical treatment relies...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2005
ISSN: 0019-2082
DOI: 10.1215/ijm/1258138137