| 1. |
- Borell, Stefan, et al.
(författare)
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Non-equivalent embeddings into complex Euclidean spaces
- 2006
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Ingår i: International Journal of Mathematics. - 0129-167X. ; 17:9, s. 1033-1046
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Tidskriftsartikel (refereegranskat)abstract
- We study the number of equivalence classes of proper holomorphic embeddings of a Stein space X into C-n. In this paper we prove that if the automorphism. group of X is a Lie group and there exists a proper holomorphic embedding of X into C-n, 0 < dim X < n, then for any k >= 0 there exist uncountably many non-equivalent proper holomorphic embeddings Φ: X x C-k hooked right arrow C-n x C-k. For k = 0 all embeddings will be proved to satisfy the additional property of C-n\Φ)(X) being (n-dim X)-Eisenman hyperbolic. As a corollary we conclude that there are uncountably many non-equivalent proper holomorphic embeddings of C-k into C-n whenever 0 < k < n.
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| 2. |
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| 3. |
- Osaka, H, et al.
(författare)
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Monotone operator functions on C*-algebras
- 2005
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Ingår i: International Journal of Mathematics. - 0129-167X. ; 16:2, s. 181-196
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Tidskriftsartikel (refereegranskat)abstract
- The article is devoted to investigation of classes of functions monotone as functions on general C-*-algebras that are not necessarily the C-*-algebra of all bounded linear operators on a Hilbert space as in classical case of matrix and operator monotone functions. We show that for general C-*-algebras the classes of monotone functions coincide with the standard classes of matrix and operator monotone functions. For every class we give exact characterization of C-*-algebras with this class of monotone functions, providing at the same time a monotonicity characterization of subhomogeneous C-*-algebras. We use this result to generalize characterizations of commutativity of a C-*-algebra based on monotonicity conditions for a single function to characterizations of subhomogeneity. As a C-*-algebraic counterpart of standard matrix and operator monotone scaling, we investigate, by means of projective C-*-algebras and relation lifting, the existence of C-*-subalgebras of a given monotonicity class.
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| 4. |
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| 5. |
- Sedykh, Vyacheslav, et al.
(författare)
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On two conjectures concerning convex curves
- 2005
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Ingår i: International Journal of Mathematics. - 0129-167X .- 1793-6519. ; 16:10, s. 1157-1173
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we recall two basic conjectures on the developables of convex projective curves, prove one of them and disprove the other in the first nontrivial case of curves in RP3. Namely, we show that i) the tangent developable of any convex curve in RP3 has degree 4 and ii) construct an example of 4 tangent lines to a convex curve in RP3 such that no real line intersects all four of them. The question (discussed in [EG1] and [So4]) whether the second conjecture is true in the special case of rational normal curves still remains open.
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| 6. |
- Seppänen, Henrik, 1976
(författare)
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TUBE DOMAINS AND RESTRICTIONS OF MINIMAL REPRESENTATIONS
- 2008
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Ingår i: International Journal of Mathematics. - 0129-167X. ; 19:10, s. 1247-1268
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study the restrictions of the minimal representation in the analytic continuation of the scalar holomorphic discrete series from Sp(n, R) to GL(+)(n, R), and from SU(n, n) to GL(n, C) respectively. We work with the realizations of the representation spaces as L-2-spaces on the boundary orbits of rank one of the corresponding cones, and give explicit integral operators that play the role of the intertwining operators for the decomposition. We prove inversion formulas for dense subspaces and use them to prove the Plancherel theorem for the respective decomposition. The Plancherel measure turns out to be absolutely continuous with respect to the Lebesgue measure in both cases.
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| 7. |
- Silvestrov, Sergei, et al.
(författare)
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Dynamical systems and commutants in crossed products
- 2007
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Ingår i: International Journal of Mathematics. - 0129-167X. ; 18:4, s. 455-471
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we describe the commutant of an arbitrary subalgebra A of the algebra of functions on a set X in a crossed product of A with the integers, where the latter act on A by a composition automorphism defined via a bijection of X. The resulting conditions which are necessary and sufficient for A to be maximal abelian in the crossed product are subsequently applied to situations where these conditions can be shown to be equivalent to a condition in topological dynamics. As a further step, using the Gelfand transform, we obtain for a commutative completely regular semi-simple Banach algebra a topological dynamical condition on its character space which is equivalent to the algebra being maximal abelian in a crossed product with the integers.
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| 8. |
- Wikström, Frank
(författare)
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The Dirichlet problem for maximal plurisubharmonic functions on analytic varieties in C^n
- 2009
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Ingår i: International Journal of Mathematics. - 0129-167X. ; 20:4, s. 521-528
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Tidskriftsartikel (refereegranskat)abstract
- Let Ω be a B-regular domain in ℂn and let V be a locally irreducible analytic variety in Ω. Given a continuous function , we prove that there is a unique maximal plurisubharmonic function u on V with boundary values given by ϕ and furthermore that u is continuous on .
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