| 1. |
- Benelkourchi, Slimane
(författare)
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A Note on the approximation of plurisubharmonic functions
- 2006
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 342:9, s. 647-650
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Tidskriftsartikel (refereegranskat)abstract
- Let Omega subset of C-n be a strongly hyperconvex domain and Omega(j) be a decreasing sequence of hyperconvex domains such that Omega = (boolean AND Omega(j))degrees. We show that every plurisubharmonic function rho is an element of F-s (Omega) is a limit of an increasing sequence of functions rho(j) is an element of F-a (Omega(j)).
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| 2. |
- Boman, Jan
(författare)
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Flatness of distributions vanishing on infinitely many hyperplanes
- 2009
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 347:23-24, s. 1351-1354
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Tidskriftsartikel (refereegranskat)abstract
- Let be a family of hyperplanes in Rn and let L0 be a limiting hyperplane of {Lk}. Let u be a distribution that satisfies a natural wave front condition and has vanishing restrictions to Lk for all k1. Then u must be flat at L0.
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| 3. |
- Bucher-Karlsson, Michelle, et al.
(författare)
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Milnor-Wood inequalities for manifolds locally isometric to a product of hyperbolic planes
- 2008
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 346:11-12, s. 661-666
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Tidskriftsartikel (refereegranskat)abstract
- This Note describes sharp Milnor-Wood inequalities for the Euler number of flat oriented vector bundles over closed Riemannian manifolds locally isometric to products of hyperbolic planes. One consequence is that such manifolds do not admit an affine structure, confirming Chern-Sullivan's conjecture in this case. The manifolds under consideration are of particular interest, since in contrary to some other locally symmetric spaces they do admit interesting flat vector bundles in the corresponding dimension. When the manifold is irreducible and of higher rank, it is shown that flat oriented vector bundles are determined completely by the sign of the Euler number.
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| 4. |
- G. Maz'ya, Vladimir
(författare)
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Boundedness of the gradient of a solution to the Neumann-Laplace problem in a convex domain
- 2009
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Ingår i: Comptes Rendus Mathematique. - : Elsevier BV. - 1631-073X. ; 347:9-10, s. 517-520
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that solutions of the Neumann problem for the Poisson equation in an arbitrary convex n-dimensional domain are uniformly Lipschitz. Applications of this result to some aspects of regularity of solutions to the Neumann problem on convex polyhedra are given. To cite this article: V. Mazya, C. R. Acad. Sci. Paris, Ser. I 347 (2009).
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| 5. |
- Gosse, L., et al.
(författare)
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Resolution of the finite Markov moment problem
- 2005
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 341:12, s. 775-780
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Tidskriftsartikel (refereegranskat)abstract
- We expose in full detail a constructive procedure to invert the so-called 'finite Markov moment problem'. The proofs rely on the general theory of Toeplitz matrices together with the classical Newton's relations.
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| 6. |
- Gustafsson, Björn, et al.
(författare)
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Bergman orthogonal polynomials on an archipelago
- 2008
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 346:9-10, s. 499-502
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Tidskriftsartikel (refereegranskat)abstract
- Growth estimates for orthogonal polynomials with respect to area measure (Bergman polynomials) over the union of finitely many Jordan regions with piecewise smooth boundary are obtained by a careful investigation of the Green function of the complement, and of Schwarz reflection in analytic arcs of the boundary. As applications we obtain a detailed picture of the limiting zero distribution of Bergman's orthogonal polynomials, and also we propose a robust reconstruction algorithm of the original open set, starting from incomplete data (such as obtained by geometric tomography).
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| 7. |
- Jin, Tianling, et al.
(författare)
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Pathological solutions to elliptic problems in divergence form with continuous coefficients
- 2009
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Ingår i: COMPTES RENDUS MATHEMATIQUE. - : Elsevier BV. - 1631-073X. ; 347:13-14, s. 773-778
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Tidskriftsartikel (refereegranskat)abstract
- We construct a function u is an element of W-loc(1.1) (B(0, 1)) which is a solution to div(A del u) = 0 in the sense of distributions, where A is continuous and u is not an element of W-loc(1.p) (B(0, 1)) for p greater than 1. We also give a function u is an element of W-loc(1.1)(B(0, 1)) such that u is an element of W-loc(1.p) (B(0, 1)) for every p less than infinity, u satisfies div(A del u) = 0 with A continuous but u is not an element of W-loc(1.infinity) (B(0, 1)). This answers questions raised by H. Brezis (On a conjecture of J. Serrin, Rend. Lincei Mat. Appl. 19 (2008) 335-338).
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| 8. |
- Karlsson, Anders, et al.
(författare)
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Liouville property and the linear drift of Brownian motion
- 2007
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 344:11, s. 685-690
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Tidskriftsartikel (refereegranskat)abstract
- Liouville property and the linear drift of Brownian motion. Let M be a complete connected Riemannian manifold with bounded sectional curvature. Under the assumption that M is a regular covering of a manifold with finite volume, we establish that M is Liouville if, and only if, the linear rate of escape of Brownian motion on M vanishes.
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| 9. |
- Kiselman, Christer O.
(författare)
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Local minima, marginal functions, and separating hyperplanes in discrete optimization
- 2008
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 346:1-2, s. 49-52
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Tidskriftsartikel (refereegranskat)abstract
- The goal of this Note is to prove results in optimization of two integer variables which correspond to fundamental results in convex analysis of real variables, viz. that a local minimum of a convex function is global; that the marginal function of a convex function is convex; and that two disjoint convex sets can be separated by a hyperplane.
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| 10. |
- Kostov, Vladimir, 1960-, et al.
(författare)
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On the Schur-Szegö composition of polynomials
- 2006
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 343:2, s. 81-86
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Tidskriftsartikel (refereegranskat)abstract
- The Schur-Szeg¨o composition of two polynomials of degree n introduces an interesting semigroup structure on polynomial spaces and is one of the basic tools in the analytic theory of polynomials, see [5]. In the present paper we show how it interacts with the stratification of polynomials according to the multiplicities of their zeros and we present the induced semigroup structure on the set of all ordered partitions of n.
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