| 1. |
- Aleman, Alexandru, et al.
(författare)
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Harmonic maps and shift-invariant subspaces
- 2021
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Ingår i: Monatshefte fur Mathematik. - : Springer Science and Business Media LLC. - 0026-9255 .- 1436-5081. ; 194:4, s. 625-656
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Tidskriftsartikel (refereegranskat)abstract
- With the help of operator-theoretic methods, we derive new and powerful criteria for finiteness of the uniton number for a harmonic map from a Riemann surface to the unitary group U(n). These use the Grassmannian model where harmonic maps are represented by families of shift-invariant subspaces of L2(S1, Cn) ; we give a new description of that model.
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| 2. |
- Brandes, Julia, 1986
(författare)
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The density of rational lines on hypersurfaces: a bihomogeneous perspective
- 2021
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Ingår i: Monatshefte für Mathematik. - : Springer Science and Business Media LLC. - 1436-5081 .- 0026-9255. ; 195:2, s. 191-231
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Tidskriftsartikel (refereegranskat)abstract
- Let F be a non-singular homogeneous polynomial of degree d in n variables. We give an asymptotic formula of the pairs of integer points (x, y) with | x| ⩽ X and | y| ⩽ Y which generate a line lying in the hypersurface defined by F, provided that n> 2 d-1d4(d+ 1) (d+ 2). In particular, by restricting to Zariski-open subsets we are able to avoid imposing any conditions on the relative sizes of X and Y.
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| 3. |
- Ganotaki, Charis, et al.
(författare)
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On eventually always hitting points
- 2021
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Ingår i: Monatshefte fur Mathematik. - : Springer Science and Business Media LLC. - 0026-9255 .- 1436-5081. ; 196:4, s. 763-784
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Tidskriftsartikel (refereegranskat)abstract
- We consider dynamical systems (X, T, μ) which have exponential decay of correlations for either Hölder continuous functions or functions of bounded variation. Given a sequence of balls (Bn)n=1∞, we give sufficient conditions for the set of eventually always hitting points to be of full measure. This is the set of points x such that for all large enough m, there is a k< m with Tk(x) ∈ Bm. We also give an asymptotic estimate as m→ ∞ on the number of k< m with Tk(x) ∈ Bm. As an application, we prove for almost every point x an asymptotic estimate on the number of k≤ m such that ak≥ mt, where t∈ (0 , 1) and ak are the continued fraction coefficients of x.
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| 4. |
- Toft, Joachim, 1964-, et al.
(författare)
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Translation and modulation invariant Hilbert spaces
- 2021
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Ingår i: Monatshefte für Mathematik (Print). - : Springer. - 0026-9255 .- 1436-5081. ; 196, s. 389-398
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Tidskriftsartikel (refereegranskat)abstract
- Let H be a Hilbert space of distributions on R-d which contains at least one non-zero element of the Feichtinger algebra S-0 and is continuously embedded in D'. If H is translation and modulation invariant, also in the sense of its norm, then we prove that H = L-2, with the same norm apart from a multiplicative constant.
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