| 1. |
- Dmytryshyn, Andrii, 1986-, et al.
(författare)
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Miniversal deformations of matrices of bilinear forms
- 2012
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Ingår i: Linear Algebra and its Applications. - : Elsevier. - 0024-3795 .- 1873-1856. ; 436:7, s. 2670-2700
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Tidskriftsartikel (refereegranskat)abstract
- Arnold [V.I. Arnold, On matrices depending on parameters, Russian Math. Surveys 26 (2) (1971) 29–43] constructed miniversal deformations of square complex matrices under similarity; that is, a simple normal form to which not only a given square matrix A but all matrices B close to it can be reduced by similarity transformations that smoothly depend on the entries of B. We construct miniversal deformations of matrices under congruence.
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| 2. |
- Zhang, Ye, 1984-, et al.
(författare)
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An optimal regularization method for convolution equations on the sourcewise represented set
- 2015
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Ingår i: Journal of Inverse and Ill-Posed Problems. - Berlin, Germany : Walter de Gruyter. - 0928-0219 .- 1569-3945. ; 23:5, s. 465-475
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Tidskriftsartikel (refereegranskat)abstract
- In this article, we consider an inverse problem for the integral equation of the convolution typein a multidimensional case. This problem is severely ill-posed. To deal with this problem, using a prioriinformation (sourcewise representation) based on optimal recovery theory we propose a new method. Theregularization and optimization properties of this method are proved. An optimal minimal a priori error ofthe problem is found. Moreover, a so-called optimal regularized approximate solution and its correspondingerror estimation are considered. Eciency and applicability of this method are demonstrated in a numericalexample of the image deblurring problem with noisy data.
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| 3. |
- Andersson, Johan, 1971-
(författare)
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Disproof of some conjectures of P. Turan
- 2007
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Ingår i: Acta Mathematica Hungarica. - : Springer Science and Business Media LLC. - 0236-5294 .- 1588-2632. ; 117:3, s. 245-250
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Tidskriftsartikel (refereegranskat)abstract
- We disprove some power sum conjectures of Turan that would have implied the density hypothesis of the Riemann zeta-function if true.
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| 4. |
- Andersson, Johan, 1971-
(författare)
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Explicit solutions to certain inf max problems from Turan power sum theory
- 2007
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Ingår i: Indagationes mathematicae. - : Elsevier. - 0019-3577 .- 1872-6100. ; 18:2, s. 189-194
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Tidskriftsartikel (refereegranskat)abstract
- In a previous paper [1] we proved that [GRAPHICS] when n + 1 is prime. In this paper we prove that [GRAPHICS] when n - 1 is a prime power, and [GRAPHICS] when n >= 3 is a prime power. We give explicit constructions of n-tuples (z(1),..., z(n)) which we prove are global minima for these problems. These are two of the few times in Turan power sum theory where solutions in the inf max problem can be explicitly calculated.
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| 5. |
- Andersson, Johan, 1971-, et al.
(författare)
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Mergelyan’s theorem with polynomials non-vanishing on unions of sets
- 2014
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Ingår i: Complex Variables and Elliptic Equations. - : Taylor & Francis. - 1747-6933 .- 1747-6941. ; 59:1, s. 99-109
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem of approximating a function having no zeros on the interior of a set by polynomials having no zeros on the entire set.
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| 6. |
- Andersson, Johan, 1971-, et al.
(författare)
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On the universality of the Epstein zeta function
- 2020
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Ingår i: Commentarii Mathematici Helvetici. - : European Mathematical Society Publishing House. - 0010-2571 .- 1420-8946. ; 95:1, s. 183-209
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Tidskriftsartikel (refereegranskat)abstract
- We study universality properties of the Epstein zeta function E-n(L,s) for lattices L of large dimension n and suitable regions of complex numbers s. Our main result is that, as n -> infinity, E-n(L,s) is universal in the right half of the critical strip as L varies over all n-dimensional lattices L. The proof uses a novel combination of an approximation result for Dirichlet polynomials, a recent result on the distribution of lengths of lattice vectors in a random lattice of large dimension and a strong uniform estimate for the error term in the generalized circle problem. Using the same approach we also prove that, as n -> infinity, E-n(L-1,s) - E-n(L-2,s) is universal in the full half-plane to the right of the critical line as E-n(L,s) varies over all pairs of n-dimensional lattices. Finally, we prove a more classical universality result for E-n(L,s) in the s-variable valid for almost all lattices L of dimension n. As part of the proof we obtain a strong bound of E-n(L,s) on the critical line that is subconvex for n >= 5 and almost all n-dimensional lattices L.
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| 7. |
- Dmytryshyn, Andrii, 1986-, et al.
(författare)
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Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence
- 2015
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Ingår i: Linear Algebra and its Applications. - : Elsevier. - 0024-3795 .- 1873-1856. ; 469, s. 305-334
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Tidskriftsartikel (refereegranskat)abstract
- We construct the Hasse diagrams G2 and G3 for the closure ordering on the sets of congruence classes of 2 × 2 and 3 × 3 complex matrices. In other words, we construct two directed graphs whose vertices are 2 × 2 or, respectively, 3 × 3 canonical matrices under congruence, and there is a directed path from A to B if and only if A can be transformed by an arbitrarily small perturbation to a matrix that is congruent to B. A bundle of matrices under congruence is defined as a set of square matrices A for which the pencils A + λAT belong to the same bundle under strict equivalence. In support of this definition, we show that all matrices in a congruence bundle of 2 × 2 or 3 × 3 matrices have the same properties with respect to perturbations. We construct the Hasse diagrams G2 B and G3 B for the closure ordering on the sets of congruence bundles of 2 × 2 and, respectively, 3 × 3 matrices. We find the isometry groups of 2 × 2 and 3 × 3 congruence canonical matrices.
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| 8. |
- Dmytryshyn, Andrii, 1986-, et al.
(författare)
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Miniversal deformations of matrices under *congruence and reducing transformations
- 2014
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Ingår i: Linear Algebra and its Applications. - : Elsevier. - 0024-3795 .- 1873-1856. ; 446:April, s. 388-420
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Tidskriftsartikel (refereegranskat)abstract
- Arnold (1971) [1] constructed a miniversal deformation of a square complex matrix under similarity; that is, a simple normal form to which not only a given square matrix A but all matrices B close to it can be reduced by similarity transformations that smoothly depend on the entries of B. We give miniversal deformations of matrices of sesquilinear forms; that is, of square complex matrices under *congruence, and construct an analytic reducing transformation to a miniversal deformation. Analogous results for matrices under congruence were obtained by Dmytryshyn, Futorny, and Sergeichuk (2012) [11].
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| 9. |
- Flodén, Lotta, et al.
(författare)
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A discussion of a homogenization procedure for a degenerate linear hyperbolic-parabolic problem
- 2017
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Ingår i: ICNPAA 2016 World Congress. - Melville, USA : American Institute of Physics (AIP). - 9780735414648
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Konferensbidrag (refereegranskat)abstract
- We study the homogenization of a hyperbolic-parabolic PDE with oscillations in one fast spatial scale. Moreover, the first order time derivative has a degenerate coefficient passing to infinity when ε → 0.We obtain a local problem which is of elliptic type, while the homogenized problem is also in some sense an elliptic problem but with the limit for ε−1∂tuε as an undetermined extra source term in the right-hand side. The results are somewhat surprising and work remains to obtain a fully rigorous treatment. Hence the last section is devoted to a discussion of the reasonability of our conjecture including numerical experiments.
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| 10. |
- Lavau, S., et al.
(författare)
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Infinity-enhancing of Leibniz algebras
- 2020
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Ingår i: Letters in Mathematical Physics. - : Springer Science and Business Media LLC. - 0377-9017 .- 1573-0530. ; 110, s. 3121-52
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Tidskriftsartikel (refereegranskat)abstract
- We establish a correspondence between infinity-enhanced Leibniz algebras, recently introduced in order to encode tensor hierarchies (Bonezzi and Hohm in Commun Math Phys 377:2027-2077, 2020), and differential graded Lie algebras, which have been already used in this context. We explain how any Leibniz algebra gives rise to a differential graded Lie algebra with a corresponding infinity-enhanced Leibniz algebra. Moreover, by a theorem of Getzler, this differential graded Lie algebra canonically induces an L-infinity-algebra structure on the suspension of the underlying chain complex. We explicitly give the brackets to all orders and show that they agree with the partial results obtained from the infinity-enhanced Leibniz algebras in Bonezzi and Hohm (Commun Math Phys 377:2027-2077, 2020).
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