| 1. |
- Ekholm, Tomas, et al.
(författare)
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Lieb-Thirring inequalities on the half-line with critical exponent
- 2008
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Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 10:3, s. 739-755
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Tidskriftsartikel (refereegranskat)abstract
- We consider the operator -d(2)/dr(2) - V in L-2(R+) with Dirichlet boundary condition at the origin. For the moments of its negative eigenvalues we prove the bound for any alpha is an element of [0, 1) and gamma >= (1 - alpha)/2. This includes a Lieb-Thirring inequality in the critical endpoint case.
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| 2. |
- Adiprasito, Karim, et al.
(författare)
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Face numbers of sequentially Cohen-Macaulay complexes and Betti numbers of componentwise linear ideals
- 2017
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society Publishing House. - 1435-9855 .- 1435-9863. ; 19:12, s. 3851-3865
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Tidskriftsartikel (refereegranskat)abstract
- A numerical characterization is given of the h-triangles of sequentially Cohen-Macaulay simplicial complexes. This result determines the number of faces of various dimensions and codimensions that are possible in such a complex, generalizing the classical Macaulay-Stanley theorem to the nonpure case. Moreover, we characterize the possible Betti tables of componentwise linear ideals. A key tool in our investigation is a bijection between shifted multicomplexes of degree <= d and shifted pure. (d - 1)-dimensional simplicial complexes.
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| 3. |
- Andreasson, Håkan, 1966, et al.
(författare)
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Proof of the cosmic no-hair conjecture in the T-3-Gowdy symmetric Einstein-Vlasov setting
- 2016
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Ingår i: Journal of the European Mathematical Society. - : EMS Publishing House. - 1435-9855 .- 1435-9863. ; 18:7, s. 1565-1650
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Tidskriftsartikel (refereegranskat)abstract
- The currently preferred models of the universe undergo accelerated expansion induced by dark energy. One model for dark energy is a positive cosmological constant. It is consequently of interest to study Einstein's equations with a positive cosmological constant coupled to matter satisfying the ordinary energy conditions: the dominant energy condition etc. Due to the difficulty of analysing the behaviour of solutions to Einstein's equations in general, it is common to either study situations with symmetry, or to prove stability results. In the present paper, we do both. In fact, we analyse, in detail, the future asymptotic behaviour of T-3-Gowdy symmetric solutions to the Einstein-Vlasov equations with a positive cosmological constant. In particular, we prove the cosmic no-hair conjecture in this setting. However, we also prove that the solutions are future stable (in the class of all solutions). Some of the results hold in a more general setting. In fact, we obtain conclusions concerning the causal structure of T-2-symmetric solutions, assuming only the presence of a positive cosmological constant, matter satisfying various energy conditions and future global existence. Adding the assumption of T-3-Gowdy symmetry to this list of requirements, we obtain C-0-estimates for all but one of the metric components. There is consequently reason to expect that many of the results presented in this paper can be generalised to other types of matter.
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| 4. |
- Canto-Martín, Francisco, et al.
(författare)
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Perron-Frobenius operators and the Klein-Gordon equation
- 2014
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Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 16:1, s. 31-66
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Tidskriftsartikel (refereegranskat)abstract
- For a smooth curve Gamma and a set Lambda in the plane R-2, let AC(Gamma; Lambda) be the space of finite Borel measures in the plane supported on Gamma, absolutely continuous with respect to arc length and whose Fourier transform vanishes on Lambda. Following [12], we say that (Gamma, Lambda) is a Heisenberg uniqueness pair if AC(Gamma; Lambda) = {0}. In the context of a hyperbola Gamma, the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets Gamma of a collection of solutions to the Klein-Gordon equation. In this work, we mainly address the issue of finding the dimension of AC(Gamma; Lambda) when it is nonzero. We will fix the curve Gamma to be the hyperbola x(1)x(2) = 1, and the set Lambda = Lambda(alpha,beta) to be the lattice-cross Lambda(alpha,beta) = (alpha Zeta x {0}) boolean OR ({0} x beta Z), where alpha, beta are positive reals. We will also consider Gamma(+), the branch of x(1)x(2) = 1 where x(1) > 0. In [12], it is shown that AC(Gamma; Lambda(alpha,beta)) = {0} if and only if alpha beta <= 1. Here, we show that for alpha beta > 1, we get a rather drastic "phase transition": AC(Gamma; Lambda(alpha,beta)) is infinite-dimensional whenever alpha beta > 1. It is shown in [13] that AC(Gamma(+); Lambda(alpha,beta)) = {0} if and only if alpha beta < 4. Moreover, at the edge alpha beta = 4, the behavior is more exotic: the space AC(Gamma(+); Lambda(alpha,beta)) is one-dimensional. Here, we show that the dimension of AC(Gamma(+); Lambda(alpha,beta)) is infinite whenever alpha beta > 4. Dynamical systems, and more specifically Perron-Frobenius operators, play a prominent role in the presentation.
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| 5. |
- Dolbeault, Jean, et al.
(författare)
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Lieb-Thirring inequalities with improved constants
- 2008
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Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 10:4, s. 1121-1126
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Tidskriftsartikel (refereegranskat)abstract
- Following Eden and Foias we obtain a matrix version of a generalised Sobolev inequality in one dimension. This allows us to improve on the known estimates of best constants in Lieb-Thirring inequalities for the sum of the negative eigenvalues for multidimensional Schrodinger operators.
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| 6. |
- Dotto, Emanuele, et al.
(författare)
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Real topological Hochschild homology
- 2021
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society - EMS - Publishing House GmbH. - 1435-9855 .- 1435-9863. ; 23:1, s. 63-152
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Tidskriftsartikel (refereegranskat)abstract
- This paper interprets Hesselholt and Madsen's real topological Hochschild homology functor THR in terms of the multiplicative norm construction. We show that THR satisfies cofinality and Morita invariance, and that it is suitably multiplicative. We then calculate its geometric fixed points and its Mackey functor of components, and show a decomposition result for group algebras. Using these structural results we determine the homotopy type of THR(F-p) and show that its bigraded homotopy groups are polynomial on one generator over the bigraded homotopy groups of H F-p. We then calculate the homotopy type of THR(Z) away from the prime 2, and the homotopy ring of the geometric fixed points spectrum Phi(Z/2) THR(Z).
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| 7. |
- Duits, Maurice, et al.
(författare)
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The two-periodic Aztec diamond and matrix valued orthogonal polynomials
- 2021
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society - EMS - Publishing House GmbH. - 1435-9855 .- 1435-9863. ; 23:4, s. 1029-1131
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Tidskriftsartikel (refereegranskat)abstract
- We analyze domino tilings of the two-periodic Aztec diamond by means of matrix valued orthogonal polynomials that we obtain from a reformulation of the Aztec diamond as a non-intersecting path model with periodic transition matrices. In a more general framework we express the correlation kernel for the underlying determinantal point process as a double contour integral that contains the reproducing kernel of matrix valued orthogonal polynomials. We use the Riemann-Hilbert problem to simplify this formula for the case of the two-periodic Aztec diamond. In the large size limit we recover the three phases of the model known as solid, liquid and gas. We describe the fine asymptotics for the gas phase and at the cusp points of the liquid-gas boundary, thereby complementing and extending results of Chhita and Johansson.
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| 8. |
- Faber, Carel, et al.
(författare)
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Relative maps and tautological classes
- 2005
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Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 7:1, s. 13-49
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Tidskriftsartikel (refereegranskat)
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| 9. |
- Farré Puiggalí, Gerard, et al.
(författare)
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Instabilities of invariant quasi-periodic tori
- 2022
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society - EMS - Publishing House GmbH. - 1435-9855 .- 1435-9863. ; 24:12, s. 4363-4383
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Tidskriftsartikel (refereegranskat)abstract
- We prove the existence of real analytic Hamiltonians with topologically unstable quasi -periodic invariant tori. Using various versions of our examples, we solve the following problems in the stability theory of analytic quasi-periodic motion:(1) Show the existence of topologically unstable tori of arbitrary frequency. Moreover, the Birkhoff Normal Form at the invariant torus can be chosen to be convergent, equal to a planar or non -planar polynomial.(2) Show the optimality of the exponential stability for Diophantine tori.(3) Show the existence of real analytic Hamiltonians that are integrable on half of the phase space, and such that all orbits on the other half accumulate at infinity.(4) For sufficiently Liouville vectors, obtain invariant tori that are not accumulated by a positive measure set of quasi-periodic invariant tori.
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| 10. |
- Hedenmalm, Håkan, 1961-, et al.
(författare)
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The Klein-Gordon equation, the Hilbert transform, and dynamics of Gauss-type maps
- 2020
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society - EMS - Publishing House GmbH. - 1435-9855 .- 1435-9863. ; 22:6, s. 1703-1757
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Tidskriftsartikel (refereegranskat)abstract
- We study the uncertainty principle associated with the Klein-Gordon equation. As in the previous work [Ann. of Math. 173 (2011)], we consider vanishing along a lattice-cross. The following variants appear naturally: (1) vanishing only along "half" of the lattice-cross, where the "half" is defined as being on the boundary of a quarter-plane, and (2) that the function vanishes on the whole lattice-cross, but we require the function to have Fourier transform supported by one of the two branches of the hyperbola. In case (1) the critical phenomenon is whether the given condition forces the function to vanish on the quarter-plane in question. Here it turns out to be crucial whether the quarter-plane is space-like or time-like, and in short the answer is yes for space-like and no for time-like. The analysis brings us quite far, involving the orbit of the Hilbert kernel under the iterates of the transfer operator, and uses methods from the theory of totally positive matrices as well as Hurwitz zeta functions, and is partially postponed to a separate publication. In case (2), the critical phenomenon occurs at another density, and the dynamics then comes from the standard Gauss transformation t bar right arrow 1/t mod Z on the interval [0, 1]. In the intermediate range of the density of the lattice-cross, we obtain unique extendability of the Fourier transform from one branch of the hyperbola to the other.
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