About the center




Related links

HUJI The Hebrew University of Jerusalem

The Edmund Landau Minerva Center for Research in Mathematical Analysis and Related Areas


List of Publications supported by the Landau Center for research in Mathematical Analysis and Related Areas

1 October 1989 -- 30 September 1990

  1. M. Ben-Artzi and A. Devinatz: Local smoothing and convergence properties of Schrödinger-type equations.

    Abstract: A local smoothing theory is developed for solutions of the initial value problem of the Schrödinger type,
    i ∂/∂t u = P(D)u, u(x,0) = u0(x).
    P(D) - self adjoint (pseudo-)differential operator. As a result, the following generalization of a result of L. Carleson was obtained:
    if u0(x) ∈ H (Rn), s > 1/2 (H - Sobolev space), then
    u(x,t) → u0 (x) as t → 0,
    almost everywhere x ∈ Rn. This is true for every elliptic or principle type symbol.

  2. M. Ben-Artzi and S. Klainerman: Decay and regularity for the Schrödinger equation.

    Abstract: The paper is concerned with certain space time estimates for the Schrödinger equation and perturbations of it. The main feature of these estimates is a certain gain of regularity which is somewhat unexpected in view of the unitary in norm L2 of the equation. The paper continues some previous work of Ben-Artzi-Devinatz and Kato-Yojima.

  3. M. Ben-Artzi: On restrictions of Fourier transforms to curved manifolds.

    Abstract: The following generalization of a theorem of Strichartz was obtained: If M is a curved manifold in Rn+1, say, of a form
    ξn = ƒ(ξ1), ξ1 = (ξ1,...,ξn),
    f(ξ1)-homogeneous, then there exists a p > 2 such that if g ∈ Lp(Rn+1) then the Fourier map g (ξ) is well defined as a map Lp(Rn+1) → L2(M).

  4. S. Ben-David, M. Magidor and S. Shelah: Trees at successors of Aronszyan singulars.

    Abstract: It is shown that a successor of a singular cardinal does not have to carry an Aronszyan tree.

  5. I. Benjamini and Y. Peres: On the Hausdorff dimension of fibers.

    Abstract: In this paper the fibres of some fractal compact plane sets are studied, and bounds on their Hausdorff dimension are obtained. The fractals investigated are intermediate between self similar fractals abd arbitrary ones. Specifically, let f be the ensemble of subsets F of the unit square obtained by partitioning it into four congruent subsquares, discarding one of them, and repeating a similar operation on the 3 remaining subsquares with no constraints on the relative positions of the discarded squares. The main results of the paper are:
    1. for all f ∈ F, dim (Fx)) ≥ 1/2, for almost all x ∈ [0,1] with respect to Lebesgue measures (here dim denotes Hausdorff dimension, and fx = {y ∈ [0,1] | (x,y) ∈ F}).
    2. for all f ∈ F and 0 ≤ α ≤ 1/2
      dim{x ∈ [0,1] | dim (Fx) ≤ α} ≤ h(α)
      where h(α) is the binary entropy.

  6. I. Benjamini and Y. Peres: Random walks on a tree and capacity in the interval.

    Abstract: The main object of this paper is to study random walks and potential theory on the boundary for trees corresponding to compact subsets of [0,1]. The correspondence is defined by the standard representation of real numbers in an integer base b > 1.
    Theorem 1 of the paper is a general transience criterion. Theorem 2 shows that transience of the random walk on a tree T(Ω,b) corresponding to a compact set Ω ⊂ [0,1] in base b, is independent of b. Theorems 3,4 and 5 are concerned with the harmonic measure μ on Ω obtained from the random walk T(Ω,b). If Ω has positive Lebesgue measure, then μ is nonsingular, while if Ω is a Lebesgue null-set, the Hausdorff dimension of μ may vanish. The logarithmic energy of μ is minimal up to a constant, but the logarithmic potential may become infinite at certain points.

  7. A. Bjorner and G. Kalai: An extended Euler-Poicare formula for regular cell complexes.
    The Klee volume.

    Abstract: A complete description of sequences of face-numbers and Betti numbers for regular cell complexes whose faces form a meet-semilattice is given. This extends the authors results on simplicial complexes (Acta Math. 161 (1988)).

  8. J. Bourgain, G. Kalai, J. Kahn, Y. Katznelson and N. Linial: The influence of variables in product spaces.
    Israel Journal of Mathematics.

  9. E. de Shalit: Differentials of the second kind on Mumford curves.
    Israel Journal of Mathematics.

    Abstract: In this paper the author uses Coleman's theory of p-adic integration to study a p-adic analytic analogue of the Hodge decomposition of the de Rahm cohomology of Mumford curves. He treats cohomology with coefficients in a local system as well. For the trivial system the author gives a new proof of Gerritzen's theorem that in a family of Mumford curves, one get a variation of Hodge structure.

  10. R. Harmelin: Hyperbolic metric, curvature of geodesics and hyperbolic discs in hyperbolic plane domains.
    Israel Journal of Mathematics, v.70 (1990), 111-128.

    Abstract: The main achievement of this paper is the establishment of precise relations among various geometric quantities such as: the uniform radii of simply-connected and of convex hyperbolic discs, the curvature of hyperbolic geodesics in multiply-connected hyperbolic plane domains and some analytic properties of the analytic covering mappings of the unit disc onto such domains.

  11. R. Harmelin: Coefficient inequalities and hyperbolic metric.

    Abstract: The author gives in this paper an interpretation of some of the most famous coefficient inequalities in geometric function theory, such as de Branges' and Loewner's inequalities, as analytic results concerning the hyperbolic metric in simply-connected and in convex domains. Generalizations of those results are also deduced for multiply-connected domains with either a positive uniform radius of convexity or a positive uniform radius of schlichtness.

  12. R. Harmelin: Covariant derivatives and conformal invariants.

    Abstract: As a consequence of a study of a duality between analytic differential operators which are invariant under a given group of Möbius mappings and differential operators which are covariant, in some sense, under the same group, the author characterizes those differential operators which are covariant either under the group of Möbius self-mappings of the unit disc of under the group of all Möbius transformations.

  13. R. Harmelin and D. Minda: Quasi-invariant domain constants.

    Abstract: The authors study five different domain constants defined for every hyperbolic plane region. One of these domain constants is a conformal invariant, while the other four are quasi-invariant under conformal mappings. For three of them the authors derive sharp bounds for their variance ratios under conformal mappings and for the last one they improve the known bound. In particular, they show all these constants may be used to characterize uniformly perfect regions in the sense of Pommerenke (Arch. Math. 32 (1979)).

  14. R. Harmelin: Covariant derivatives and automorphic forms.

    Abstract: In this paper two types of differential operators are constructed and studied, both of which produce automorphic forms of any order form any give automorphic function or form, for any Kleinian group. The first type of these operators is related to the hyperbolic metric in a given invariant region under the group, while the other one is independent of the choice of the invariant region.

  15. R. Harmelin: Generalizations of Ahlfors-Weil's quasiconformal extension.

    Abstract: The author generalizes both Becker's and Ahlfors-Weill's quasiconformal extensions and studies them in order to deduce new criteria for the existence of quasiconformal extensions for a given meromorphic function in a half plane.

  16. G. Kalai: On low-dimensional faces that high-dimensional polytopes must have.
    Combinatorica 10 (1990).

    Abstract: A typical result: Every 5-dimensional polytype has a 2-dimensional face which is a quadrangle or a triangle. This solves a problem of Perles and Shephard from 1965 as well as a problem of Danzer from 1982.

  17. G. Kalai: On the number of faces of centrally-symmetric convex polytopes.
    Graphs and Combinatorics 5 (1989), 389-391.

    Abstract: The following conjecture is presented and discussed: Every centrally symmetric d-polytope has at least 3d faces.

  18. G. Kalai: The diameter of graphs of convex polytopes and f-vector theory.
    The Klee volume.

    Abstract: The porpose of this paper is to discuss a relation between the diameter problem for simple polytopes and f-vectors of simplicial polytopes and the subcomplexes of their boundary complexes. This is done via the recent concept of magnifying properties of graphs. The authors prove a far-reaching generalization of the upper bound theorem and use this result to prove a magnifying property, and a polynomial bound on the diameter for graphs of dual-to-neighborly polytopes. They also prove the generalized lower bound inequalities for a large class of simplicial spheres.

  19. G. Kalai: Upper bound theorems, the diameter problem and algebraic shifting.
    The Nagoya Conference on Commutative Algebra and Combinatorics (1990).

    Abstract: This surveys the previous item.

  20. R. Kenyon and Y. Peres: Intersecting random translates of invariant Cantor sets.

    Abstract: The authors study the Hausdorff dimension of intersections (X+t) ∩ Y, when X,Y are Cantor sets invariant under the map x → bx mod 1. This dimension is constant almost everywhere in t. When X,Y are defined by Sofic systems in base b, this constant is computed in terms of the Lyapunov exponent of a random product of matrices.

  21. Y. Kifer: Equilibrium states and large deviations for random transformations.

    Abstract: The main theorem establishes the uniqueness of equilibrium states for expanding in average random transformations which is the first result about uniqueness of a maximizing measure in the relativized variational principle. This implies relativized large deviation estimates for such trasformations.

  22. S. Klainerman: Remarks on the asyptotic behaviour of the Klein-Gordon equation in Rn+1.

    Abstract: The paper is concerned with the asymptotic behaviour of the linear Klein-Gordon equation. The paper follows previous work of the author and L. Hörmander which was based on the invariant properties of the equation and simple energy estimates. In this paper the author uses similar methods to show that the decay of the solutions are stronger along null rays than along time-like ones.

  23. Y.S. Kupitz: On a generalization of Gallai-Sylvesters theorem.
    Discrete and Computational Geometry.

    Abstract: The author proves that km + 1 [km + 2] affinely independent points in R2m+1 [R2m] span a hyperplane avoiding (at least) k points of the set. Set of km [km + 1] points in R2m+1 [R2m] not spanning such a hyperplane are characterzed using Stan Hansen's theorem and results from a classical paper by Kelly and Moser. A similar problem in the plane over the complexes C2 is solved using a result of Hirzebruch (based on Miyoka-Yan inequalities - noted by L.M. Kelly in his recent resolution of the Serre conjecture).

  24. Y.S. Kupitz: A note on a conves segment in a triangulation.
    Discrete Mathematics.

    Abstract: An inner edge e of a planar triangulation σ is convex if the two triangles having e as a common edge is a convex set. The author proves that the maximal number of convex segments in a triangulation over all triangulations σ having n boundary verticles and m inner vertices is
    [1/2(5m + min(m,n -2))]

  25. Y.S. Kupitz: k-bisectors of a planar set.

    Abstract: The author proves using Helly theorem that any 3k + 1 point in R2, spanning R2, span a line on each open side of which there are at least k points of the set.

  26. Y.S. Kupitz: Separation of a finite set in d-space by spanned hyperplanes.

    Abstract: The main result is that any affinely independent 4k + 1 points in R3 span a plane on each open side of which there are at least k points of the set. Sets of 4k affinely independent points in R3 not spanning such a plane are characterized. Generalization to d-space are discussed.

  27. Y.S. Kupitz and M.A. Perles: Extremal theory for conves matchings in convex geometric graphs.

    Abstract: The authors determine the maximal number of edges in a convex geometric graph of order n(≥ 3) not containing a convex l-matching (l ≥ 2) as a spanning subgraph. They also determine the minimal number of edges in a convex geometric graph which is saturated relatively to the above property (i.e., not containing a convex l-matching but with the additions of any edge this property is violated).

  28. Y.S. Kupitz: On the existence of a Schlegel diagram of a simplicial unstacked 3-polytope with a prescirbed set of vertices.

    Abstract: The author shows that except for two well defined configurations any planar set V such that
    #(∂[V ∩ V) = 3 is the Schlegel diagram of a simplicial unstacked polytope.

  29. Y.S. Kupitz: k-supporting hyperplanes of a finite set in d-space.

    Abstract: The main result is that for all k,d ≥ 1 any set of [1/2(d + 1)k] + 1 affinely independent points in d-space span a hyperplane supporting the whole set but still avoiding at least k points of the set. Sets of [1/2(d + 1)k] points not spanning such a hyperplane are characterized.

  30. Y.S. Kupitz and M.A. Perles: Locally symmetric graphs.

    Abstract: An n-regular graph G is locally symmetric if Aut(G) acts as Sn on the n neighbours of each vertex. The authors classify such graphs having 4-cycles as the shortest cycle (girth 4). They discuss and produce such graphs for girths 5,6,7, the latter example is based on a famous tesselation of the hyperbolic plane given by Klein in 1879.

  31. A. Lubotzky and S. Mozes: Vanishing of matrix coefficients for representations of tree automeorisms.

    Abstract: An analogue of the Howe-Moore theorem is proved for the automorphism group of a tree is proven. i.e., in any unitary representation of this group which has no invariant non-zero vectors the matrix coefficients tend to zero at infinity.

  32. S. Mozes and Y. Peres: Joinings of Bernoulli processes.

    Abstract: The main result of the paper asserts that: If Z is any ergodic process and X,Y are nontrivial Bernoulli processes such that h(X) + h(Y) > h(Z) (h(W) means the entropy of the process W) then there exists a joining of X and Y having Z as a factor.

  33. S. Mozes: Actions of simple Lie groups are mixing of all orders.

    Abstract: It is proved that irreducible actions of semi simple Lie groups on a probability space are mixing of all orders.

  34. B. Peleg and J. Rosenmüller: The least-core, nucleolus, and kernel of homogeneous weighted majority games.

    Abstract: Homogeneous weighted majority games were already introduced by von Neumann and Morgenstern ; They discussed uniqueness of the representation and the "main simple solution" for constant-sum games. For the same class of games, Peleg studied the kernel and the nucleolus. Ostmann and Rosenmüller described the nature of representations of general homogeneous weighted majority games. The present paper starts out to close the gap: for the general homogeneous weighted majority game "without steps", we discuss the least core, the nucleolus, and the kernel and show their close relationship (coincidence) with the unique minimal representation.

  35. E. Rips: Finitely generated pseudogroups of partial isometrics of an interval.

    Abstract: For the pseudogroups mentioned in the title, a structure theory is developed. The central result is a decomposition theorem, which enables to reduce the study of such pseudogroups to pseudogroups of several simpler types. The obtained results are then used in the theory of groups of isometrics of R-trees.

  36. Z. Sela: The homeomorphism problem for geometric 3-manifolds and equations in hyperbolic groups.

    Abstract: The question of deciding whether two "given" manifolds are homeomorphic by an "effective" algorithm is being treated. Even though the notions "given" and "effective" need to be specified, it's aggreed that the question is solvable in dimension 2 and unsolvable for dimensions n ≥ 4. By reducing systems of equations from hyperbolic groups to free groups one is able to provide an algorithm for the homeomorphism problem for 3-manifolds satisfying a weaker hypothesis than the Thurston geometrization conjecture. The paper uses Makanin-Razbarov algorithm for solving equations in free groups as well as techniques from group actions on trees and 3-dimensional topology.

  37. Z. Sela: Dehn fillings that reduce Thurston norm.
    Israel Journal of Mathematics 69 (1990).

    Abstract: Sutured manifolds machinery developed by David Gabbai turned out to be one of the applicable theories in knot theory over the recent years. One of its main theorems is that for Φp atoroidal 3-manifold all but at most one Dehn filling do not reduce the Thurston norm of specific second homology class. In this paper one looks at the whole second homology group (i.e. not a specific class). Examples for which more that one Dehn filling reduces the Thurston norm of (distinct) second homology classes are being constructed. Their number is bounded by the number of faces of the Thurston ball.

  38. S. Shelah: Kaplansky test problem for modules.
    Israel Journal of Mathematics.

    Abstract: In Shelah, the classical Kaplansky first test problem is solved for the class of R-modules for any given (not necessarily commutative) ring. This tells us that in the cases not already well understood (R a left pure semisimple ring) decompositions behave badly.

Edmund Landau Back to the Landau Center's home page
Back to the Math home page

Last updated: Aug. 2nd, 2004

Copyright ©2004 , The Hebrew University of Jerusalem. All Rights Reserved.