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Vol.27 (1) 2005 — 5 results found.

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A classification theorem for certain actions of $\mathbb{R}$ on $C^*$-algebras
C. R. Math. Rep. Acad. Sci. Canada Vol. 27, (1), 2005 pp. 25–32
Andrew J. Dean (Received: 2004/10/06)

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It is shown that two \(C^*\)-dynamical systems of the form \((K\otimes A, \mathbb{R}, \mathrm{Ad} U\otimes id)\), where \(U\) is a unitary representation of \(\mathbb{R}\) that decomposes as a finite direct sum of non-trivial irreducible representations whose multiplicities have greatest common denominator 1, and \(A\) is a simple, unital \(C^*\)-algebra with real rank zero and cancellation, are equivariantly isomorphic if, and only if, the two representations are unitarily equivalent. As a corollary, a classification result for certain inductive limit type actions of \(\mathbb{R}\) on stable UHF algebras is given.

Il est montré que deux systèmes \(C^*\)-dynamiques de la forme \((K\otimes A, \mathbb{R}, \mathrm{Ad} U\otimes id)\) où \(U\) est une representation unitaire de \(\mathbb{R}\), qui décompose comme une somme directe et finie des representations non-triviales et irréductibles dont les multiplicités ont 1 comme le dénominateur commun et le plus grand, et \(A\) est un \(C^*\)-algèbre simple, avec l’unité et avec rang réel zéro et annullation, sont isomorphe équivariantement si et seulement si les deux representations sont équivalentes unitairement. Comme un corollaire, un résultat classification pour quelques actions du type de la limite inductive de \(\mathbb{R}\) sur les algèbres d’UHF stables est aussi donné.

Eisenstein Equations and Central Norms
C. R. Math. Rep. Acad. Sci. Canada Vol. 27, (1), 2005 pp. 20–24
R.A. Mollin (Received: 2004/06/14)

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Central norms are given definition according to the infrastructure of the underlying order under discussion, which we define in the introductory section below. We relate these central norms in the simple continued fraction expansion of \(\sqrt{D}\) to solutions of the Eisenstein equation \(x^2-Dy^2 = -4\), with \(\gcd(x,y) = 1\). This provides a criterion for central norms to be \(4\) in the presence of certain congruence conditions on the fundamental unit of the underlying real quadratic order \(\mathbb{Z}[\sqrt{D}]\).

Hidden structure of the Lie algebra of symmetries
C. R. Math. Rep. Acad. Sci. Canada Vol. 27, (1), 2005 pp. 14–19
O.I. Bogoyavlenskij (Received: 2004/02/25)

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For any dynamical system, a hidden structure of its Lie algebra of symmetries is disclosed. The structure is based on a new infinite series of the canonically defined Lie subalgebras and on their commutator relations.

Pour n’importe quel système dynamique, une structure cachée de son algèbre de Lie de symétries est révélée. Cette structure découle d’une nouvelle série de sous-algèbres de Lie canoniquement définies et de leurs relations de commutateurs.

Radial Distribution of Zeros of Entire Functions and Sections of their Power Series
C. R. Math. Rep. Acad. Sci. Canada Vol. 27, (1), 2005 pp. 8–13
Faruk F. Abi-Khuzam; May F. Hamdan (Received: 2003/11/11)

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For an entire function \(f\) with non-negative Maclaurin coefficients, a region is obtained which is defined in terms of Hayman’s function \(b(r) = r (rf^{\prime} (r)/f(r))^{\prime}\), and which is free of all zeros of \(f\) and those of all its sections. The new region defined improves on previous results. In particular, it is shown that when \(\underset{n\rightarrow \infty}{\limsup}\, b(r) = A^2/4\), \(A>0\), then the zeros \(r_n \exp (i\theta_n)\) of \(f\) satisfy the inequality, \(\underset{n\rightarrow \infty}{\liminf}\, |\theta_n| \geq 4\sin^{-1} (1/A\sqrt{2})\), which is very close to being optimal.

Etant donnée une function entière \(f\) avec des coéfficients positifs, on trouve une région définie en termes de la fonction \(b(r) = r (rf^{\prime}(r)/f(r))^{\prime}\) de Hayman, dépourvue des zéros de \(f\) et de ceux de toutes ses sections. Particulièrement, on démontre qu’au cas où \(\underset{n\rightarrow \infty}{\limsup}\, b(r) = A^2/4\), \(A>0\), les zéros \(r_n \exp (i\theta_n)\) de \(f\) satisfont l’inégalité \(\underset{n\rightarrow\infty}{\liminf} \, |\theta_n| \geq 4\sin^{-1} (1/A\sqrt{2})\), qui est presque optimale.

Exact controllability of the wave equation in fractional order spaces
C. R. Math. Rep. Acad. Sci. Canada Vol. 27, (1), 2005 pp. 2–7
Kalifa Bodian; Abdoulaye Sene; Mary Teuw Niane (Received: 2004/09/01)

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We define norm estimates for the trace of solution of the wave equation with initial conditions in irregular Sobolev spaces of fractional order. Then exact controllability results are deduced.

On établit des estimations de normes pour la trace de la solution de l’équation des ondes avec des données initiales dans des espaces de Sobolev non réguliers et à puissances fractionnaires. On déduit les résultats de contrôlabilité exacte correspondants.

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Most used Keywords

algebraic number theory approximation property automorphisms Bessel functions Boson-fermion correspondence C*-algebra Carmichael number center problem Chebyshev transform Classification of simple C*-algebras composition operators continued fractions Cuntz Semigroup elliptic curves fixed point Fourier transform function fields. functoriality general relativity generic property ideals indefinite inner product inductive limits of sub-homogeneous C*- algebras Irrational rotation algebra J-Hermitian matrix K-theory Kahler manifolds L-functions maximal ideal space nonexpansive mapping noninterlacing numerical range orthogonal polynomials Predual space prime number property SP quadratic forms Renormalization rotation algebras Salem number semi-reciprocal polynomials tracially approximate splitting interval algebras unbounded traces Weak Markov set Whitney problems

Most used AMS

05C05 11A07 11A55 11B37 11B68 11D09 11D25 11D41 11E04 11F67 11G05 11R09 11R11 13B25 14J26 14M25 14P10 17B37 17B67 19K56 26A51 30C15 30H05 35B 37E10 37E20 37F20 37F25 39B72 42C05 43A07 43A62 46B20 46L05 46L35 46L40 46L55 46L80 47H10 53B25 53C55 54C60 60F10 60J75 83C05

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