| 1. |
- Aleman, Alexandru, et al.
(författare)
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Continuous deformations of harmonic maps and their unitons
- 2019
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Ingår i: Monatshefte fur Mathematik. - : Springer Science and Business Media LLC. - 0026-9255 .- 1436-5081.
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Tidskriftsartikel (refereegranskat)abstract
- It is known that any harmonic map of finite uniton number from a Riemann surface into U (n) can be deformed into a new harmonic map with an associated S1-invariant extended solution. We study this deformation in detail using operator-theoretic methods. In particular, we show that the corresponding unitons are real analytic functions of the deformation parameter, and that the deformation is closely related to the Bruhat decomposition of the corresponding extended solution.
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| 2. |
- 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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| 3. |
- 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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| 4. |
- Coriasco, Sandro, et al.
(författare)
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Local wave-front sets of Banach and Fréchet types, and pseudo-differential operators
- 2013
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Ingår i: Monatshefte für Mathematik (Print). - : Springer. - 0026-9255 .- 1436-5081. ; 169:3-4, s. 285-316
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Tidskriftsartikel (refereegranskat)abstract
- Let ω, ω 0 be appropriate weight functions and ${\fancyscript{B}}$ be an invariant BF-space. We introduce the wave-front set ${{\rm WF}_{\mathcal{B}}(f)}$ with respect to the weighted Fourier Banach space ${\mathcal{B}=\fancyscript{F} \fancyscript{B}(\omega )}$ . We prove that the usual mapping properties for pseudo-differential operators Op t (a) with symbols a in ${S^{(\omega_0)}_{\rho, 0}}$ hold for such wave-front sets. In particular we prove ${{\rm WF}_{\mathcal C}({\rm Op}_t (a) f)\subseteq {\rm WF}_{\mathcal{B}}(f)}$ and ${{\rm WF}_{\mathcal{B}}(f) \subseteq {\rm WF} _{\mathcal C}({\rm Op}_t (a) f)\bigcup {\rm Char} (a)}$ . Here ${\mathcal{C}=\fancyscript{F} \fancyscript{B}(\omega /\omega_0)}$ and Char(a) is the set of characteristic points of a.
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| 5. |
- Ernvall-Hytönen, Anna Maria, et al.
(författare)
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Formulas for the number of gridlines
- 2011
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Ingår i: Monatshefte für Mathematik (Print). - : Springer. - 0026-9255 .- 1436-5081. ; 164:2, s. 157-170
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Tidskriftsartikel (refereegranskat)abstract
- Let l(n) be the number of lines through at least two points of an n × n rectangular grid. We prove recursive and asymptotic formulas for it using respectively combinatorial and number theoretic methods. We also study the ratio l(n)/l(n - 1). All this originates from Mustonen's experimental results.
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| 6. |
- Fischer, V., et al.
(författare)
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Degenerate principal series representations of SO(p+1, p)
- 2015
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Ingår i: Monatshefte Fur Mathematik. - : Springer Science and Business Media LLC. - 0026-9255 .- 1436-5081. ; 176:1, s. 87-105
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Tidskriftsartikel (refereegranskat)abstract
- For odd, the Lie group has a family of complementary series representations realized on the space of real skew symmetric matrices, similar to the Stein's complementary series for . We consider their restriction on the subgroup and prove that they are still irreducible and is equivalent to (a unitarization of) the principal series representation of , and also irreducible under a maximal parabolic subgroup of G.
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| 7. |
- Färm, David
(författare)
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Simultaneously non-convergent frequencies of words in different expansions
- 2011
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Ingår i: Monatshefte für Mathematik. - : Springer Science and Business Media LLC. - 0026-9255 .- 1436-5081. ; 162:4, s. 409-427
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Tidskriftsartikel (refereegranskat)abstract
- We consider expanding maps such that the unit interval can be represented as a full symbolic shift space with bounded distortion. There are already theorems about the Hausdorff dimension for sets defined by the set of accumulation points for the frequencies of words in one symbolic space at a time. We show that the dimension is preserved when such sets defined using different maps are intersected. More precisely, it is proven that the dimension of any countable intersection of sets defined by their sets of accumulation for frequencies of words in different expansions, has dimension equal to the infimum of the dimensions of the sets that are intersected. As a consequence, the set of numbers for which the frequencies do not exist has full dimension even after countable intersections. We also prove that this holds for a dense set of non-integer base expansions.
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| 8. |
- 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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| 9. |
- Gustafsson, Björn, et al.
(författare)
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On the curvature of the free boundary for the obstacle problem in two dimensions
- 2004
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Ingår i: Nonlinear Differential Equation Models. - : Springer Science and Business Media LLC. - 3211209956 ; 142:02-jan, s. 1-5
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Konferensbidrag (refereegranskat)abstract
- We give a new proof of the fact that the free boundary for the obstacle problem in two dimensions satisfies a natural and sharp inner ball condition.
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| 10. |
- Hakobyan, A., et al.
(författare)
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Nonlinear free boundary problems with singular source terms
- 2004
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Ingår i: Monatshefte für Mathematik (Print). - : Springer Science and Business Media LLC. - 0026-9255 .- 1436-5081. ; 142:1-2, s. 7-16
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Tidskriftsartikel (refereegranskat)abstract
- We prove the existence of solutions to nonlinear free boundary problem with singularities at given points.
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