| 1. |
- Alaghmandan, Mahmood, 1983, et al.
(författare)
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Completely bounded maps and invariant subspaces
- 2020
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 1432-1823 .- 0025-5874. ; 294:1-2, s. 471-489
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Tidskriftsartikel (refereegranskat)
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| 2. |
- Aleman, Alexandru, et al.
(författare)
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Symmetric shift-invariant subspaces and harmonic maps
- 2021
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 299:1-2, s. 183-202
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Tidskriftsartikel (refereegranskat)abstract
- The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an important class of harmonic maps into symmetric and k-symmetric spaces. Using an appropriate description of such symmetric shift-invariant subspaces we obtain new results for the corresponding extended solutions, including how to obtain primitive harmonic maps from certain harmonic maps into the unitary group.
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| 3. |
- Andersson, Mats, 1957, et al.
(författare)
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On non-proper intersections and local intersection numbers
- 2022
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 300:1, s. 1019-1039
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Tidskriftsartikel (refereegranskat)abstract
- Given equidimensional (generalized) cycles mu(1) and mu(2) on a complex manifold Y we introduce a product mu(1) lozenge Y mu(2) that is a generalized cycle whose multiplicities at each point are the local intersection numbers at the point. If Y is projective, then given a very ample line bundle L -> Y we define a product mu(1)circle L mu(2) whose multiplicities at each point also coincide with the local intersection numbers. In addition, provided that mu(1) and mu(2) are effective, this product satisfies a Bezout inequality. If i : Y -> P-N is an embedding such that i* O(1) = L, then mu(1)circle L mu(2) can be expressed as a mean value of Stuckrad-Vogel cycles on P-N. There are quite explicit relations between lozenge Y and circle L.
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| 4. |
- Bergweiler, Walter, et al.
(författare)
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The Hausdorff dimension of Julia sets of meromorphic functions in the Speiser class
- 2022
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 302:4, s. 2193-2205
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Tidskriftsartikel (refereegranskat)abstract
- We show that for each d∈ (0 , 2] there exists a meromorphic function f such that the inverse function of f has three singularities and the Julia set of f has Hausdorff dimension d.
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| 5. |
- Björklund, Michael, 1981, et al.
(författare)
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Aperiodic order and spherical diffraction, II: translation bounded measures on homogeneous spaces
- 2021
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 1432-1823 .- 0025-5874. ; In Press
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Tidskriftsartikel (refereegranskat)abstract
- We study the auto-correlation measures of invariant random point processes in the hyperbolic plane which arise from various classes of aperiodic Delone sets. More generally, we study auto-correlation measures for large classes of Delone sets in (and even translation bounded measures on) arbitrary locally compact homogeneous metric spaces. We then specialize to the case of weighted model sets, in which we are able to derive more concrete formulas for the auto-correlation. In the case of Riemannian symmetric spaces we also explain how the auto-correlation of a weighted model set in a Riemannian symmetric space can be identified with a (typically non-tempered) positive-definite distribution on R-n. This paves the way for a diffraction theory for such model sets, which will be discussed in the sequel to the present article.
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| 6. |
- Björn, Anders, et al.
(författare)
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Sharp Besov capacity estimates for annuli in metric spaces with doubling measures
- 2023
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Ingår i: Mathematische Zeitschrift. - : SPRINGER HEIDELBERG. - 0025-5874 .- 1432-1823. ; 305:3
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Tidskriftsartikel (refereegranskat)abstract
- We obtain precise estimates, in terms of the measure of balls, for the Besov capacity of annuli and singletons in complete metric spaces. The spaces are only assumed to be uniformly perfect with respect to the centre of the annuli and equipped with a doubling measure.
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| 7. |
- Björn, Anders, et al.
(författare)
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The Liouville theorem for p-harmonic functions and quasiminimizers with finite energy
- 2021
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Ingår i: Mathematische Zeitschrift. - : SPRINGER HEIDELBERG. - 0025-5874 .- 1432-1823. ; 297:1-2, s. 827-854
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Tidskriftsartikel (refereegranskat)abstract
- We show that, under certain geometric conditions, there are no nonconstant quasiminimizers with finite pth power energy in a (not necessarily complete) metric measure space equipped with a globally doubling measure supporting a global p-Poincare inequality. The geometric conditions are that either (a) the measure has a sufficiently strong volume growth at infinity, or (b) the metric space is annularly quasiconvex (or its discrete version, annularly chainable) around some point in the space. Moreover, on the weighted real line R, we characterize all locally doubling measures, supporting a local p-Poincare inequality, for which there exist nonconstant quasiminimizers of finite p-energy, and show that a quasiminimizer is of finite p-energy if and only if it is bounded. As p-harmonic functions are quasiminimizers they are covered by these results.
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| 8. |
- Casarino, V., et al.
(författare)
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On the maximal operator of a general Ornstein-Uhlenbeck semigroup
- 2022
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 301, s. 2393-2413
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Tidskriftsartikel (refereegranskat)abstract
- If Q is a real, symmetric and positive definite n x n matrix, and B a real n x n matrix whose eigenvalues have negative real parts, we consider the Ornstein-Uhlenbeck semigroup on R-n with covariance Q and drift matrix B. Our main result says that the associated maximal operator is of weak type (1, 1) with respect to the invariant measure. The proof has a geometric gist and hinges on the "forbidden zones method" previously introduced by the third author.
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| 9. |
- Chen, Chih-Whi, et al.
(författare)
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Translated simple modules for Lie algebras and simple supermodules for Lie superalgebras
- 2021
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Ingår i: Mathematische Zeitschrift. - : Springer Nature. - 0025-5874 .- 1432-1823. ; 297:1-2, s. 255-281
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Tidskriftsartikel (refereegranskat)abstract
- We prove that the tensor product of a simple and a finite dimensional sln-module has finite type socle. This is applied to reduce classification of simple q(n)-supermodules to that of simple sln-modules. Rough structure of simple q(n)-supermodules, considered as sln-modules, is described in terms of the combinatorics of category O.
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| 10. |
- Chen, Qinbo, et al.
(författare)
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On simultaneous linearization of certain commuting nearly integrable diffeomorphisms of the cylinder
- 2022
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Ingår i: Mathematische Zeitschrift. - : Springer Nature. - 0025-5874 .- 1432-1823. ; 301:2, s. 1881-1912
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Tidskriftsartikel (refereegranskat)abstract
- Let F and K be commuting C∞ diffeomorphisms of the cylinder T× R that are, respectively, close to F(x, y) = (x+ ω(y) , y) and Tα(x, y) = (x+ α, y) , where ω(y) is non-degenerate and α is Diophantine. Using the KAM iterative scheme for the group action we show that F and K are simultaneously C∞-linearizable if F has the intersection property (including the exact symplectic maps) and K satisfies a semi-conjugacy condition. We also provide examples showing necessity of these conditions. As a consequence, we get local rigidity of certain class of Z2-actions on the cylinder, generated by commuting twist maps.
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