On fixed point free involutions of
Gerhard X. Ritter (1976)
Colloquium Mathematicae
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Gerhard X. Ritter (1976)
Colloquium Mathematicae
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Uffe Haagerup, Hanne Schultz (2009)
Publications Mathématiques de l'IHÉS
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Let ℳ be a von Neumann factor of type II1 with a normalized trace τ. In 1983 L. G. Brown showed that to every operator T∈ℳ one can in a natural way associate a spectral distribution measure μ T (now called the Brown measure of T), which is a probability measure in ℂ with support in the spectrum σ(T) of T. In this paper it is shown that for every T∈ℳ and every Borel set B in ℂ, there is a unique closed T-invariant subspace affiliated with ℳ, such that the Brown measure of is concentrated...
Rüdiger Göbel, Daniel Herden, Saharon Shelah (2014)
Journal of the European Mathematical Society
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It is a well-known fact that modules over a commutative ring in general cannot be classified, and it is also well-known that we have to impose severe restrictions on either the ring or on the class of modules to solve this problem. One of the restrictions on the modules comes from freeness assumptions which have been intensively studied in recent decades. Two interesting, distinct but typical examples are the papers by Blass [1] and Eklof [8], both jointly with Shelah. In the first case...
Martin Arkowitz, Mauricio Gutierrez (2002)
Fundamenta Mathematicae
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If f:G → H is a group homomorphism and p,q are the projections from the free product G*H onto its factors G and H respectively, let the group be the equalizer of fp and q:G*H → H. Then p restricts to an epimorphism . A right inverse (section) of is called a coaction on G. In this paper we study and the sections of . We consider the following topics: the structure of as a free product, the restrictions on G resulting from the existence of a coaction, maps of coactions and...
Marek Bożejko, Gero Fendler (2006)
Banach Center Publications
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We show that for the t-deformed semicircle measure, where 1/2 < t ≤ 1, the expansions of functions with respect to the associated orthonormal polynomials converge in norm when 3/2 < p < 3 and do not converge when 1 ≤ p < 3/2 or 3 < p. From this we conclude that natural expansions in the non-commutative spaces of free group factors and of free commutation relations do not converge for 1 ≤ p < 3/2 or 3 < p.
Przemysław Liszka (2013)
Annales Polonici Mathematici
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Let for i = 1,..., N be contracting similarities, let be a probability vector and let ν be a probability measure on with compact support. It is well known that there exists a unique inhomogeneous self-similar probability measure μ on such that . We give satisfactory estimates for the lower and upper bounds of the spectra of inhomogeneous self-similar measures. The case in which there are a countable number of contracting similarities and probabilities is considered. In particular,...
Giuseppe Cordaro (2007)
Studia Mathematica
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We consider the perturbed Neumann problem ⎧ -Δu + α(x)u = α(x)f(u) + λg(x,u) a.e. in Ω, ⎨ ⎩ ∂u/∂ν = 0 on ∂Ω, where Ω is an open bounded set in with boundary of class C², with , f: ℝ → ℝ is a continuous function and g: Ω × ℝ → ℝ, besides being a Carathéodory function, is such that, for some p > N, and for all t ∈ ℝ. In this setting, supposing only that the set of global minima of the function has M ≥ 2 bounded connected components, we prove that, for all λ ∈ ℝ small enough,...
Nikolay Nikolov, László Pyber (2011)
Journal of the European Mathematical Society
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We first note that a result of Gowers on product-free sets in groups has an unexpected consequence: If is the minimal degree of a representation of the finite group , then for every subset of with we have . We use this to obtain improved versions of recent deep theorems of Helfgott and of Shalev concerning product decompositions of finite simple groups, with much simpler proofs. On the other hand, we prove a version of Jordan’s theorem which implies that if , then has a...
A. Ivić (1975)
Matematički Vesnik
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Giovanni Anello, Giuseppe Cordaro (2003)
Colloquium Mathematicae
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We present two results on existence of infinitely many positive solutions to the Neumann problem ⎧ in Ω, ⎨ ⎩ ∂u/∂ν = 0 on ∂Ω, where is a bounded open set with sufficiently smooth boundary ∂Ω, ν is the outer unit normal vector to ∂Ω, p > 1, μ > 0, with and f: Ω × ℝ → ℝ is a Carathéodory function. Our results ensure the existence of a sequence of nonzero and nonnegative weak solutions to the above problem.
Bo'az Klartag (2010)
Journal of the European Mathematical Society
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Suppose that is an absolutely continuous probability measure on n, for large . Then has low-dimensional marginals that are approximately spherically-symmetric. More precisely, if , then there exist -dimensional marginals of that are -far from being sphericallysymmetric, in an appropriate sense. Here is a universal constant.
Anna Grimaldi Piro, Francesco Ragnedda (1991)
Annales Polonici Mathematici
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Abstract. We study a Neumann problem for the heat equation in a cylindrical domain with -base and data in , a subspace of 1. We derive our results, considering the action of an adjoint operator on , a predual of , and using known properties of this last space.
Krzysztof Zajkowski (2010)
Studia Mathematica
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We prove that for the spectral radius of a weighted composition operator , acting in the space , the following variational principle holds: , where X is a Hausdorff compact space, α: X → X is a continuous mapping preserving a Borel measure μ with suppμ = X, is the set of all α-invariant ergodic probability measures on X, and a: X → ℝ is a continuous and -measurable function, where . This considerably extends the range of validity of the above formula, which was previously known...
Mats Andersson (2011)
Bulletin de la Société Mathématique de France
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Let be a coherent subsheaf of a locally free sheaf and suppose that has pure codimension. Starting with a residue current obtained from a locally free resolution of we construct a vector-valued Coleff-Herrera current with support on the variety associated to such that is in if and only if . Such a current can also be derived algebraically from a fundamental theorem of Roos about the bidualizing functor, and the relation between these two approaches is discussed....
Yihong Du, Bendong Lou (2015)
Journal of the European Mathematical Society
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We study nonlinear diffusion problems of the form with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundary representing the expanding front. For special of the Fisher-KPP type, the problem was investigated by Du and Lin [DL]. Here we consider much more general nonlinear terms. For any which is and satisfies , we show that the omega limit set of every bounded positive solution is determined by a stationary...
Philippe Clément, Wolfgang Desch (2008)
Studia Mathematica
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Let , be complete separable metric spaces. Denote by (X) the space of probability measures on X, by the p-Wasserstein metric with some p ∈ [1,∞), and by the space of probability measures on X with finite Wasserstein distance from any point measure. Let , , be a Borel map such that f is a contraction from into . Let ν₁,ν₂ be probability measures on Ω with finite. On X we consider the subordinated measures . Then . As an application we show that the solution measures ...
Huaning Liu, Hui Dong (2015)
Czechoslovak Mathematical Journal
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A positive integer is called a square-free number if it is not divisible by a perfect square except . Let be an odd prime. For with , the smallest positive integer such that is called the exponent of modulo . If the exponent of modulo is , then is called a primitive root mod . Let be the characteristic function of the square-free primitive roots modulo . In this paper we study the distribution and give an asymptotic formula by using properties of character...
E. Ferreyra, T. Godoy, M. Urciuolo (2002)
Colloquium Mathematicae
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Let , 1 ≤ i ≤ n, and for t > 0 and x = (x₁,...,xₙ) ∈ ℝⁿ, let , and . Let φ₁,...,φₙ be real functions in such that φ = (φ₁,..., φₙ) satisfies φ(t • x) = t ∘ φ(x). Let γ > 0 and let μ be the Borel measure on given by , where and dx denotes the Lebesgue measure on ℝⁿ. Let and let be the operator norm of from into , where the spaces are taken with respect to the Lebesgue measure. The type set is defined by . In the case for 1 ≤ i,k ≤ n we characterize the...
Teodor Banica (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
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Associated to an Hadamard matrix is the spectral measure μ ∈ [0,N] of the corresponding Hopf image algebra, A = C(G) with . We study a certain family of discrete measures , coming from the idempotent state theory of G, which converge in Cesàro limit to μ. Our main result is a duality formula of type , where are the truncations of the spectral measures μ,ν associated to . We also prove, using these truncations , that for any deformed Fourier matrix we have μ = ν.
Huishi Li (2015)
Commentationes Mathematicae Universitatis Carolinae
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Let be a (noncommutative) solvable polynomial algebra over a field in the sense of A. Kandri-Rody and V. Weispfenning [Non-commutative Gröbner bases in algebras of solvable type, J. Symbolic Comput. 9 (1990), 1–26]. This paper presents a comprehensive study on the computation of minimal free resolutions of modules over in the following two cases: (1) is an -graded algebra with the degree-0 homogeneous part ; (2) is an -filtered algebra with the filtration determined by...
Marius Dadarlat, Wilhelm Winter (2008)
Bulletin de la Société Mathématique de France
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Suppose is a separable unital -algebra each fibre of which is isomorphic to the same strongly self-absorbing and -injective -algebra . We show that and are isomorphic as -algebras provided the compact Hausdorff space is finite-dimensional. This statement is known not to extend to the infinite-dimensional case.
Julien Melleray (2014)
Annales de l’institut Fourier
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We show that, whenever is a countable abelian group and is a finitely-generated subgroup of , a generic measure-preserving action of on a standard atomless probability space extends to a free measure-preserving action of on . This extends a result of Ageev, corresponding to the case when is infinite cyclic.
M. Prizzi, M. Rinaldi, K. P. Rybakowski (2002)
Studia Mathematica
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Consider the family uₜ = Δu + G(u), t > 0, , , t > 0, , of semilinear Neumann boundary value problems, where, for ε > 0 small, the set is a thin domain in , possibly with holes, which collapses, as ε → 0⁺, onto a (curved) k-dimensional submanifold of . If G is dissipative, then equation has a global attractor . We identify a “limit” equation for the family , prove convergence of trajectories and establish an upper semicontinuity result for the family as ε → 0⁺. ...