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Vol.34 (1) 2012 — 3 results found.

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Note on Poincaré $L^p$ Type Inequality for Differential Forms on Semialgebraic Sets
C. R. Math. Rep. Acad. Sci. Canada Vol. 34 (1) 2012, pp. 23–32
Leonid Shartser (Received: 2011/06/02)

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We study local and global Poincaré type \(L^p\) inequalities on a compact semialgebraic subset of \(\mathbb{R}^n\) for \(p\gg 1\). As a consequence, we obtain an isomorphism between \(L^p\) cohomology and singular cohomology of a normal compact semialgebraic set. The global inequality is derived from the local one, while the local inequality is proved by means of a semialgebraic Lipschitz deformation retraction with estimates on its derivatives.

On étudie les inégalités locales et globales de type \(L^p\) de Poincaré sur un sous-ensemble compact semialgébrique de \(\mathbb{R}^n\) pour \(p\gg 1\). Par conséquent, nous obtenons un isomorphisme entre la cohomologie \(L^p\) et la cohomologie singulière d’un ensemble normal compact semialgébrique. L’inégalité globale est dérivée de la locale, tandis que l’inégalité locale est prouvée au moyen d’une rétraction de déformation semialgébrique Lipschitz avec des estimations sur ses dérivés.

The Radical Approach to Infinitesimals in Historical Perspective
C. R. Math. Rep. Acad. Sci. Canada Vol. 34 (1) 2012, pp. 9–22
Joachim Lambek (Received: 2011/08/17)

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Homomorphisms from the Fredholm Semigroup to Abelian Semigroups
C. R. Math. Rep. Acad. Sci. Canada Vol. 34 (1) 2012, pp. 1–8
George A. Elliott; Brian Skinner (Received: 2010/04/18, Revised: 2011/08/15)

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It is shown that the universal enveloping abelian semigroup of the semigroup of Fredholm operators on an infinite-dimensional Hilbert space is the group of integers.

On démontre que l’index de Fredholm est le morphisme universel du semigroupe d’opérateurs de Fredholm sur un espace de Hilbert de dimension infinie dans un semigroupe abélien.

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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 cycles of ideals elliptic curves fixed point Fourier transform function fields. 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

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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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