On semigroups of -endomorphisms
Iwanik, Anzelm
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Iwanik, Anzelm
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Cédric Arhancet (2013)
Studia Mathematica
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We give sufficient conditions on an operator space E and on a semigroup of operators on a von Neumann algebra M to obtain a bounded analytic or R-analytic semigroup ( on the vector valued noncommutative -space . Moreover, we give applications to the functional calculus of the generators of these semigroups, generalizing some earlier work of M. Junge, C. Le Merdy and Q. Xu.
Ralph deLaubenfels (2009)
Studia Mathematica
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Suppose A is an injective linear operator on a Banach space that generates a uniformly bounded strongly continuous semigroup . It is shown that generates an -regularized semigroup. Several equivalences for generating a strongly continuous semigroup are given. These are used to generate sufficient conditions on the growth of , on subspaces, for generating a strongly continuous semigroup, and to show that the inverse of -d/dx on the closure of its image in L¹([0,∞)) does not generate...
Radu Ignat, Felix Otto (2008)
Journal of the European Mathematical Society
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In this paper, we study a model for the magnetization in thin ferromagnetic films. It comes as a variational problem for -valued maps (the magnetization) of two variables : . We are interested in the behavior of minimizers as . They are expected to be -valued maps of vanishing distributional divergence , so that appropriate boundary conditions enforce line discontinuities. For finite , these line discontinuities are approximated by smooth transition layers, the so-called Néel...
Yoichi Motohashi (1970)
Acta Arithmetica
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Bérenger Akon Kpata, Ibrahim Fofana, Konin Koua (2010)
Colloquium Mathematicae
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Let d be a positive integer and μ a generalized Cantor measure satisfying , where , , with 0 < ρ < 1 and R an orthogonal transformation of . Then ⎧1 < p ≤ 2 ⇒ ⎨, , ⎩ p = 2 ⇒ infr≥1 rd(1/α’-1/2) (∫J₀r|μ̂(y)|² dy)1/2 ≥ D₂ρd/α’where , α’ is defined by and the constants D₁ and D₂ depend only on d and p.
Svetlana Roudenko (2004)
Studia Mathematica
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We determine the duals of the homogeneous matrix-weighted Besov spaces and which were previously defined in [5]. If W is a matrix weight, then the dual of can be identified with and, similarly, . Moreover, for certain W which may not be in the class, the duals of and are determined and expressed in terms of the Besov spaces and , which we define in terms of reducing operators associated with W. We also develop the basic theory of these reducing operator Besov spaces....
Tai-Wei Chen, Chung-I Ho, Jyh-Haur Teh (2016)
Commentationes Mathematicae Universitatis Carolinae
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For a double complex , we show that if it satisfies the -lemma and the spectral sequence induced by does not degenerate at , then it degenerates at . We apply this result to prove the degeneration at of a Hodge-de Rham spectral sequence on compact bi-generalized Hermitian manifolds that satisfy a version of -lemma.
Miloš Arsenović, Dragoljub Kečkić (2006)
Studia Mathematica
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We consider elementary operators , acting on a unital Banach algebra, where and are separately commuting families of generalized scalar elements. We give an ascent estimate and a lower bound estimate for such an operator. Additionally, we give a weak variant of the Fuglede-Putnam theorem for an elementary operator with strongly commuting families and , i.e. (), where all and ( and ) commute. The main tool is an L¹ estimate of the Fourier transform of a certain class...
Adam Bobrowski, Radosław Bogucki (2008)
Studia Mathematica
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Let be a locally compact Hausdorff space. Let , i = 0,1,...,N, be generators of Feller semigroups in C₀() with related Feller processes and let , i = 0,...,N, be non-negative continuous functions on with . Assume that the closure A of defined on generates a Feller semigroup T(t), t ≥ 0 in C₀(). A natural interpretation of a related Feller process X = X(t), t ≥ 0 is that it evolves according to the following heuristic rules: conditional on being at a point p ∈ , with probability...
Victoria Knopova (2004)
Colloquium Mathematicae
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The aim of the paper is two-fold. First, we investigate the ψ-Bessel potential spaces on and study some of their properties. Secondly, we consider the fractional powers of an operator of the form , , where is an operator with real continuous negative definite symbol ψ: ℝⁿ → ℝ. We define the domain of the operator and prove that with this domain it generates an -sub-Markovian semigroup.
Jan Kisyński (2011)
Bulletin of the Polish Academy of Sciences. Mathematics
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Characterizations of equicontinuity and convergent sequences are given for the space of rapidly decreasing distributions and the space of slowly increasing infinitely differentiable functions.
Stanislav Jakubec (1994)
Mathematica Slovaca
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M. Anbudurai, R. Parvatham, S. Ponnusamy, V. Singh (2004)
Annales Polonici Mathematici
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Let A denote the space of all analytic functions in the unit disc Δ with the normalization f(0) = f’(0) − 1 = 0. For β < 1, let . For λ > 0, suppose that denotes any one of the following classes of functions: , , . The main purpose of this paper is to find conditions on λ and γ so that each f ∈ is in or , γ ∈ [0,1/2]. Here and respectively denote the class of all starlike functions of order γ and the class of all convex functions of order γ. As a consequence, we obtain...
(2013)
Colloquium Mathematicae
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We consider one-parameter (C₀)-semigroups of operators in the space with infinitesimal generator of the form where G is an -valued rapidly decreasing distribution on ℝⁿ. It is proved that the Petrovskiĭ condition for forward evolution ensures not only the existence and uniqueness of the above semigroup but also its nice behaviour after restriction to whichever of the function spaces , , p ∈ [1,∞], , a ∈ ]0,∞[, or the spaces , q ∈ ]1,∞], of bounded distributions.
Jean Mawhin, Katarzyna Szymańska-Dębowska (2016)
Mathematica Bohemica
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A couple () of lower and upper slopes for the resonant second order boundary value problem with increasing on such that , is a couple of functions such that for all , in the stripe and . It is proved that the existence of such a couple implies the existence and localization of a solution to the boundary value problem. Multiplicity results are also obtained.