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Vol.30 (2) 2008 — 4 results found.

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Remarks on some recent fixed point theorems
C. R. Math. Rep. Acad. Sci. Canada Vol. 30 (2) 2008, pp. 56–63
S.L. Singh; Rajendra Pant (Received: 2007/10/09)

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We obtain fixed and common point theorems generalizing fixed point theorems of W. A. Kirk and T. Suzuki for Banach and Meir–Keeler type asymptotic contractions.

Nous démontrons des théorèmes de points fixes et de points communs qui généralisent des théorèmes de points fixes du type de Banach et de Meir–Keeler pour les contractions asymptotiques.

Diophantine inequality for equicharacteristic excellent Henselian local domains
C. R. Math. Rep. Acad. Sci. Canada Vol. 30 (2) 2008, pp. 48–55
Hirotada Ito; Shuzo Izumi (Received: 2008/01/07, Revised: 2008/03/30)

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G. Rond has proved a Diophantine type inequality for the field of quotients of the convergent or formal power series ring in multivariables. We generalize his theorem to the field of the quotients of an excellent Henselian local domain in equicharacteristic case.

G. Rond a démontré une inégalité de type diophantien pour le corps des quotients de séries convergentes (ou formelles) à plusieurs variables. On fait ici une généralisation de son théorème au corps des quotients d’un anneau local intégral henselien excellent dans le cas équi-caractéristique.

Factorization of an indefinite convection-diffusion operator
C. R. Math. Rep. Acad. Sci. Canada Vol. 30 (2) 2008, pp. 40–47
Marina Chugunova; Vladimir Strauss (Received: 2008/02/04)

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We prove that a certain non-self-adjoint differential operator admits factorization, and we apply this new representation of the operator to explicitly construct its domain. We also show that the operator is J-self-adjoint in a Krein space.

On montre qu’un certain opérateur non autoadjoint admet une factorisation et, on utilise cette représentation pour construire explicitement son domaine. On montre aussi que cet opérateur est J-autoadjoint dans un espace de Krein.

Hypergroups with unique $\alpha$-means
C. R. Math. Rep. Acad. Sci. Canada Vol. 30 (2) 2008, pp. 33–39
Ahmadreza Azimifard (Received: 2007/08/18)

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Let \(K\) be a commutative hypergroup and \(\alpha\in \widehat{K}\). We show that \(K\) is \(\alpha\)-amenable with the unique \(\alpha\)-mean \(m_\alpha\) if and only if \(m_\alpha \in L^1(K) \cap L^2(K)\) and \(\alpha\) is isolated in \(\widehat{K}\). In contrast to the case of amenable noncompact locally compact groups, examples of polynomial hypergroups with unique \(\alpha\)-means (\(\alpha \not= 1\)) are given. Further examples emphasize that the \(\alpha\)-amenability of hypergroups depends heavily on the asymptotic behavior of Haar measures and characters.

Soit \(K\) un hypergroupe commutatif et \(\alpha\in \widehat{K}\). Nous montrons que \(K\) est \(\alpha\)-moyennable avec unicité de l’\(\alpha\)-moyenne \(m_\alpha\) si et seulement si \(m_\alpha \in L^1(K) \cap L^2(K)\) et \(\alpha\) est isolé dans \(\widehat{K}\). Contrairement au cas des groupes moyennables localement compacts mais non compacts, des exemples d’hyper-groupes polynomiaux avec unicité des \(\alpha\)-moyennes (\(\alpha \not= 1\)) sont donnés. Nous montrons à l’aide d’autres examples que l’\(\alpha\)-moyennabilité des hypergroupes dépend fortement de leurs mesures de Haar ainsi que du comportement des caractères.

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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 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 numerical range orthogonal polynomials Predual space prime number property SP Renormalization rotation algebras Salem number semi-reciprocal polynomials tracially approximate splitting interval algebras unbounded traces uniqueness Weak Markov set Whitney problems

Most used AMS

05C05 11A07 11A55 11B37 11B68 11D09 11D25 11D41 11E04 11F11 11F66 11F67 11G05 11R09 11R11 13B25 14J26 14M25 14P10 17B37 17B67 19K14 19K56 26A51 30C15 30H05 35B 37E10 37E20 37F25 39B72 42C05 43A07 46B20 46L05 46L35 46L40 46L55 46L80 47H10 53B25 53C55 54C60 60F10 83C05

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