# Digitala Vetenskapliga Arkivet

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• 1.
University of Missouri.
University of Missouri. Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology. University of Missouri. University of Missouri.
Sharp Geometric Maximum Principles for Semi-Elliptic Operators with Singular Drift2011In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 18, no 4, p. 613-620Article in journal (Refereed)

We discuss a sharp generalization of the Hopf-Oleinik boundary point principle (BPP) for domains satisfying an interior pseudo-ball condition, for non-divergence form, semi-elliptic operators with singular drift. In turn, this result is used to derive a version of the strong maximum principle under optimal pointwise blow-up conditions for the coefficients of the differential operator involved. We also explain how a uniform two-sided pseudo-ball condition may be used to provide a purely geometric characterization of Lyapunov domains, and clarify the role this class of domains plays vis-a-vis to the BPP.

• 2. Ammann, Bernd
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Harmonic spinors and local deformations of the metric2011In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 18, no 5, p. 927-936Article in journal (Refereed)

Let (M, g) be a compact Riemannian spin manifold. The Atiyah-Singer index theorem yields a lower bound for the dimension of the kernel of the Dirac operator. We prove that this bound can be attained by changing the Riemannian metric g on an arbitrarily small open set.

• 3. Benguria, Rafael D.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space2008In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 15, no 4, p. 613-622Article in journal (Refereed)

It is shown that the sharp constant in the Hardy-Sobolev-Maz'ya inequality on the upper half space H-3 subset of R-3 is given by the Sobolev constant. This is achieved by a duality argument relating the problem to a Hardy-Littlewood-Sobolev type inequality whose sharp constant is determined as well.

• 4.
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
On polynomial eigenfunctions for a class of differential operators2002In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 9, p. 153-171Article in journal (Refereed)
• 5. Borell, Stefan
Proper Holomorphic Disks in the Complement of Varieties in C22008In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 15, no 4, p. 821-826Article in journal (Refereed)
• 6. Bouarroudj, Sofiane
Stockholm University, Faculty of Science, Department of Mathematics.
Lie algebra deformations in characteristic 22015In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 22, no 2, p. 353-402Article in journal (Refereed)

Of four types of Kaplansky algebras, type-2 and type-4 algebras have previously unobserved Z/2-gradings: nonlinear in roots. A method assigning a simple Lie superalgebra to every Z/2-graded simple Lie algebra in characteristic 2 is illustrated by seven new series. Type-2 algebras and one of the two type-4 algebras are demystified as nontrivial deforms (the results of deformations) of the alternate Hamiltonian algebras. The type-1 Kaplansky algebra is recognized as the derived of the nonalternate version of the Hamiltonian Lie algebra, the one that preserves a tensorial 2-form. Deforms corresponding to nontrivial cohomology classes can be isomorphic to the initial algebra, e.g., we confirm Grishkov's implicit claim and explicitly describe the Jurman algebra as such a semitrivial deform of the derived of the alternate Hamiltonian Lie algebra. This paper helps to sharpen the formulation of a conjecture describing all simple finite-dimensional Lie algebras over any algebraically closed field of nonzero characteristic and supports a conjecture of Dzhumadildaev and Kostrikin stating that all simple finite-dimensional modular Lie algebras are either of standard type or deforms thereof. In characteristic 2, we give sufficient conditions for the known deformations to be semitrivial.

• 7. Bridy, Andrew
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Finite ramification for preimage fields of post-critically finite morphisms2017In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 24, no 6, p. 1633-1647Article in journal (Refereed)

Given a finite endomorphism phi of a variety X defined over the field of fractions K of a Dedekind domain, we study the extension K (phi(-infinity)(alpha)) := boolean OR(n >= 1) K (phi(-n) (alpha)) generated by the preimages of alpha under all iterates of phi. In particular when phi is post-critically finite, i.e., there exists a non-empty, Zariski-open W subset of X such that phi(-1) (W) subset of W and phi : W -> X is etale, we prove that K (phi(-infinity) (alpha)) is rami fied over only finitely many primes of K. This provides a large supply of in finite extensions with restricted rami fication, and generalizes results of Aitken-Hajir-Maire [1] in the case X = A(1) and Cullinan-Hajir, Jones-Manes [7, 13] in the case X = P-1. Moreover, we conjecture that this finite rami fication condition characterizes post-critically finite morphisms, and we give an entirely new result showing this for X = P-1. The proof relies on Faltings' theorem and a local argument.

• 8.
Independent University of Moscow.
Stockholm University, Faculty of Science, Department of Mathematics.
Around matrix-tree theorem2006In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Math. Res. Lett., Vol. 13, no 5--6, p. 761-774Article in journal (Refereed)

Generalizing the classical matrix-tree theorem we provide a formula counting subgraphs of a given graph with a fixed 2-core. We use this generalization to obtain an analog of the matrix-tree theorem for the root system Dn (the classical theorem corresponds to the An-case). Several byproducts of the developed technique, such as a new formula for a specialization of the multivariate Tutte polynomial, are of independent interest.

FULLTEXT01
• 9. Costa, L.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Derived category of fibrations2011In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 18, no 3, p. 425-432Article in journal (Refereed)

In this paper we give a structure theorem for the derived category D(b)(X) of a Zariski locally trivial fibration X over Z with fiber F provided both F and Z have a full strongly exceptional collection of line bundles.

• 10.
Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Indecomposable manipulations with simple modules in category O2019In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 26, no 2, p. 447-499Article in journal (Refereed)

We study the problem of indecomposability of translations of simple modules in the principal block of BGG category O for sl(n), as conjectured in [KiM1]. We describe some general techniques and prove a few general results which may be applied to study various special cases of this problem. We apply our results to verify indecomposability for n <= 6. We also study the problem of indecomposability of shufflings and twistings of simple modules and obtain some partial results.

• 11. Friedlander, John B.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
PRODUCTS IN RESIDUE CLASSES2008In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 15, no 5-6, p. 1133-1147Article in journal (Refereed)

We consider a problem of P. Erdos, A. M. Odlyzko and A. Sarkozy about the representation of residue classes modulo m by products of two not too large primes. While it seems that even the Extended Riemann Hypothesis is not powerful enough to achieve the expected results, here we obtain some unconditional results "on average" over moduli m and residue classes modulo m and somewhat stronger results when the average is restricted to prime moduli m = p. We also consider the analogous question wherein the primes are replaced by easier sequences so, quite naturally, we obtain much stronger results.

• 12.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Lower bounds for the weak type (1, 1) estimate for the maximal function associated to cubes in high dimensions2013In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 20, no 5, p. 907-918Article in journal (Refereed)

In this paper, we will provide the quantitative estimation for the dependence of a lower bound of the Hardy-Littlewood maximal function. This work was inspired by the paper [1] of Stein and Strömberg where general properties of the maximal function were studied. In that work, the increase with the dimension d of the constant Ad that appears in the weak type (1, 1) inequality for the maximal function was proved however no estimation were given. In a recent paper [2], J.M. Aldaz showed that the lowest constant Ad tends to infinity as the dimension d → ∞. In this paper, we improve the result of J.M. Aldaz providing quantitative estimation of Ad ≥ Cd1/4, where C is a constant independent of d.

• 13.
Malmö högskola, Faculty of Technology and Society (TS).
Quasi-normal modes for de Sitter–Reissner–Nordström black holes2017In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 24, no 1, p. 83-117Article in journal (Refereed)

The quasi-normal modes for black holes are the resonances for the scattering of incoming waves by black holes. Here we consider scattering of massless uncharged Dirac fields propagating in the outer region of de Sitter-Reissner-Nordstr¨om black hole, which is spherically symmetric charged exact solution of the Einstein-Maxwell equations. Using the spherical symmetry of the equation and restricting to a fixed harmonic the problem is reduced to a scattering problem for the 1D massless Dirac operator on the line. The resonances for the problem are related to the resonances for a certain semiclassical Schr¨odinger operator with exponentially decreasing positive potential. We give exact relation between the sets of Dirac and Schr¨odinger resonances. The asymptotic distribution of the resonances is close to the lattice of pseudopoles associated to the non-degenerate maxima of the potentials. Using the techniques of quantum Birkhoff normal form we give the complete asymptotic formulas for the resonances. In particular, we calculate the first three leading terms in the expansion. Moreover, similar results are obtained for the de Sitter-Schwarzschild quasi-normal modes, thus improving the result of S´a Barreto and Zworski in [2].

• 14. Johansson, Anders
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
Square summability of variations of g-functions and uniqueness of g-measures2003In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 10, no 5-6, p. 587-601Article in journal (Refereed)
• 15.
University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
Square summability of variations of g-functions and uniqueness of g-measures2003In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 10, no 5, p. 587-601Article in journal (Refereed)

We prove uniqueness of $g$-measures for $g$-functions satisfying quadratic summability of variations. Our result is in contrast to the situation of, \eg, the one-dimensional Ising model with long-range interactions, since $\ell_1$-summability of variations is required for general potentials. We illustrate this difference with some examples. To prove our main result we use a product martingale argument. We also give conditions for uniqueness of general $G$-measures, \ie, the case for general potentials, based on our investigation of the probabilistic case involving $g$-functions.

• 16.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
On the recursive structure of Branson's Q-curvature2014In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 21, no 3, p. 495-507Article in journal (Refereed)
• 17.
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
Boundary behavior of solutions to linear and nonlinear elliptic equations in plane convex domains2001In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 8, no 1-2, p. 189-193Article in journal (Refereed)
• 18.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
On the fixed points of the map x→xx modulo a prime2015In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 22, no 1, p. 141-168Article in journal (Refereed)

In this paper, we show that for almost all primes p there is an integer solution xε [2,p-1] to the congruence xx ≡ x (mod p). The solutions can be interpretated as fixed points of the map x→xx (mod p), and we study numerically and discuss some unexpected properties of the dynamical system associated with this map.

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