| 1. |
- Ben Said, S., et al.
(författare)
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Invariant trilinear forms on spherical principal series of real rank one semisimple Lie groups
- 2014
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Ingår i: International Journal of Mathematics. - : World Scientific Pub Co Pte Lt. - 0129-167X .- 1793-6519. ; 25:3
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Tidskriftsartikel (refereegranskat)abstract
- Let G be a connected semisimple real-rank one Lie group with finite center. We consider intertwining operators on tensor products of spherical principal series representations of G. This allows us to construct an invariant trilinear form K. indexed by a complex multiparameter (v)under bar = (v1, v2, v3) and defined on the space of smooth functions on the product of three spheres in F-n, where F is either R, C, H, or O with n = 2. We then study the analytic continuation of the trilinear form with respect to (v1, v2, v3), where we locate the hyperplanes containing the poles. Using a result due to Johnson and Wallach on the so-called "partial intertwining operator", we obtain an expression for the generalized Bernstein-Reznikov integral K-(v) under bar (1 circle times 1 circle times 1) in terms of hypergeometric functions.
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| 2. |
- Berman, Robert, 1976
(författare)
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Bergman kernels and equilibrium measures for polarized pseudoconcave domains
- 2010
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Ingår i: International Journal of Mathematics. - 0129-167X. ; 21:1, s. 77-115
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Tidskriftsartikel (refereegranskat)abstract
- Let X be a domain in a closed polarized complex manifold (Y, L), where L is a (semi-) positive line bundle over Y. Any given Hermitian metric on L induces by restriction to X a Hilbert space structure on the space of global holomorphic sections on Y with values in the k-th tensor power of L (also using a volume form omega(n) on X). In this paper the leading large k asymptotics for the corresponding Bergman kernels and metrics are obtained in the case when X is a pseudo-concave domain with smooth boundary (under a certain compatibility assumption). The asymptotics are expressed in terms of the curvature of L and the boundary of X. The convergence of the Bergman metrics is obtained in a more general setting where (X, omega(n)) is replaced by any measure satisfying a Bernstein-Markov property. As an application the (generalized) equilibrium measure of the polarized pseudo-concave domain X is computed explicitly. Applications to the zero and mass distribution of random holomorphic sections and the eigenvalue distribution of Toeplitz operators will be described elsewhere.
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| 3. |
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| 4. |
- Hansen, Frank, et al.
(författare)
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Generalized noncommutative Hardy and Hardy-Hilbert type inequalities
- 2010
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Ingår i: International Journal of Mathematics. - 0129-167X. ; 21:10, s. 1283-1295
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Tidskriftsartikel (refereegranskat)abstract
- We extend and unify several Hardy type inequalities to functions whose values are positive semi-definite operators. In particular, our methods lead to the operator versions of Hardy-Hilbert's and Godunova's inequalities. While classical Hardy type inequalities hold for parameter values p > 1, it is typical that the operator versions hold only for 1 < p ≤ 2, even for functions with values in 2 × 2 matrices.
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| 5. |
- Hed, Lisa
(författare)
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Approximation of negative plurisubharmonic functions with given boundary values
- 2010
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Ingår i: International Journal of Mathematics. - 0129-167X. ; 21:9, s. 1135-1145
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study the approximation of negative plurisubharmonic functions with given boundary values. We want to approximate a plurisubharmonic function by an increasing sequence of plurisubharmonic functions defined on strictly larger domains.
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| 6. |
- Lundström, Patrik, 1971-, et al.
(författare)
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Skew category algebras associated with partially defined dynamical systems
- 2012
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Ingår i: International Journal of Mathematics. - 0129-167X. ; 23:4, s. 16-
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Tidskriftsartikel (refereegranskat)abstract
- We introduce partially defined dynamical systems defined on a topological space. To each such system we associate a functor s from a category G to Top^op and show that it defines what we call a skew category algebra AxG. We study the connection between topological freeness of s and, on the one hand, ideal properties of AxG and, on the other hand, maximal commutativity of A in AxG. In particular, we show that if G is a groupoid and for each e in ob(G) the group of all morphisms from e to e is countable and the topological space s(e) is Tychonoff and Baire, then the following assertions are equivalent: (i) s is topologically free; (ii) A has the ideal intersection property, that is if I is a nonzero ideal of AxG, then I \cap A is not equal to zero; (iii) the ring A is a maximal abelian complex subalgebra of AxG. Thereby, we generalize a result by Svensson, Silvestrov and de Jeu from the additive group of integers to a large class of groupoids.
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| 7. |
- Menegon, Aurelio
(författare)
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Le’s polyhedron for line singularities
- 2014
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Ingår i: International Journal of Mathematics. - : World Scientific. - 0129-167X .- 1793-6519. ; 25:13
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Tidskriftsartikel (refereegranskat)abstract
- We study the topology of line singularities, which are complex hypersurface germs with non-isolated singularity given by a smooth curve. We describe the degeneration of its Milnor fiber to the singular hypersurface by means of a vanishing polyhedron in the Milnor fiber. As a milestone, we also study the topology of the degeneration of a complex isolated singularity hypersurface under a nonlocal point of view.
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| 8. |
- Samko, Natasha
(författare)
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On two-weight estimates for the maximal operator in local Morrey spaces
- 2014
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Ingår i: International Journal of Mathematics. - 0129-167X. ; 25:11
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Tidskriftsartikel (refereegranskat)abstract
- For two weighted local Morrey spaces and we obtain general type sufficient conditions and necessary conditions imposed on the functions φ and ψ and the weights u and v for the boundedness of the maximal operator from to , with some "logarithmic gap" between the sufficient and necessary conditions. Both the conditions formally coincide if we omit a certain logarithmic factor in these conditions.
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