Preprints
List of Publications supported by the Landau Center for research in
Mathematical Analysis and Related Areas
1 October 1989  30 September 1990
 M. BenArtzi and A. Devinatz: Local smoothing and convergence
properties of Schrödingertype 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 u_{0}(x) ∈ H (R^{n}), s > 1/2
(H  Sobolev space), then
u(x,t) → u_{0} (x) as t → 0,
almost everywhere x ∈ R^{n}.
This is true for every elliptic or principle type symbol.
 M. BenArtzi 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 BenArtziDevinatz and KatoYojima.
 M. BenArtzi: 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 R^{n+1},
say, of a form
ξ_{n} = ƒ(ξ1), ξ1 = (ξ1,...,ξ_{n}),
f(ξ1)homogeneous, then there exists a p > 2 such that if
g ∈ L^{p}(R^{n+1}) then the Fourier
map g (ξ) is well
defined as a map L^{p}(R^{n+1}) →
L^{2}(M).
 S. BenDavid, 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.
 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:
 for all f ∈ F, dim (F_{x})) ≥ 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}).
and
 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.
 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 nullset, 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.
 A. Bjorner and G. Kalai: An extended EulerPoicare formula for
regular cell complexes.
The Klee volume.
 Abstract:
A complete description of sequences of facenumbers and Betti numbers for
regular cell complexes whose faces form a meetsemilattice is given. This
extends the authors results on simplicial complexes
(Acta Math. 161 (1988)).
 J. Bourgain, G. Kalai, J. Kahn, Y. Katznelson and N. Linial:
The influence of variables in product spaces.
Israel Journal of Mathematics.
 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 padic integration to
study a padic 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.
 R. Harmelin: Hyperbolic metric, curvature of geodesics and
hyperbolic discs in hyperbolic plane domains.
Israel Journal of Mathematics, v.70 (1990), 111128.
 Abstract:
The main achievement of this paper is the establishment of precise relations
among various geometric quantities such as: the uniform radii of
simplyconnected and of convex hyperbolic discs, the curvature of hyperbolic
geodesics in multiplyconnected hyperbolic plane domains and some analytic
properties of the analytic covering mappings of the unit disc onto such
domains.
 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 simplyconnected and in convex domains. Generalizations of those
results are also deduced for multiplyconnected domains with either a positive
uniform radius of convexity or a positive uniform radius of schlichtness.
 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 selfmappings of the unit
disc of under the group of all Möbius transformations.
 R. Harmelin and D. Minda: Quasiinvariant 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 quasiinvariant 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)).
 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.
 R. Harmelin: Generalizations of AhlforsWeil's quasiconformal
extension.
 Abstract:
The author generalizes both Becker's and AhlforsWeill'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.
 G. Kalai: On lowdimensional faces that highdimensional polytopes
must have.
Combinatorica 10 (1990).
 Abstract:
A typical result: Every 5dimensional polytype has a 2dimensional 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.
 G. Kalai: On the number of faces of centrallysymmetric convex
polytopes.
Graphs and Combinatorics 5 (1989), 389391.
 Abstract:
The following conjecture is presented and discussed: Every centrally symmetric
dpolytope has at least 3^{d} faces.
 G. Kalai: The diameter of graphs of convex polytopes and
fvector theory.
The Klee volume.
 Abstract:
The porpose of this paper is to discuss a relation between the diameter problem
for simple polytopes and fvectors 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 farreaching
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
dualtoneighborly polytopes. They also prove the generalized lower bound
inequalities for a large class of simplicial spheres.
 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.
 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.
 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.
 S. Klainerman: Remarks on the asyptotic behaviour of the
KleinGordon equation in R^{n+1}.
 Abstract:
The paper is concerned with the asymptotic behaviour of the linear
KleinGordon 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 timelike ones.
 Y.S. Kupitz: On a generalization of GallaiSylvesters theorem.
Discrete and Computational Geometry.
 Abstract:
The author proves that km + 1 [km + 2] affinely independent points in
R^{2m+1} [R^{2m}]
span a hyperplane avoiding (at least)
k points of the set. Set of km [km + 1] points in
R^{2m+1} [R^{2m}]
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
C^{2}
is solved using a result of Hirzebruch (based on MiyokaYan
inequalities  noted by L.M. Kelly in his recent resolution of the Serre
conjecture).
 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))]
 Y.S. Kupitz: kbisectors of a planar set.
 Abstract:
The author proves using Helly theorem that any 3k + 1 point in
R^{2}, spanning R^{2},
span a line on each open side of
which there are at least k points of the set.
 Y.S. Kupitz: Separation of a finite set in dspace by
spanned hyperplanes.
 Abstract:
The main result is that any affinely independent 4k + 1 points in
R^{3}
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 R^{3}
not spanning such a plane are characterized. Generalization
to dspace are discussed.
 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 lmatching
(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 lmatching
but with the additions of any edge this property is violated).
 Y.S. Kupitz: On the existence of a Schlegel diagram of a simplicial
unstacked 3polytope 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.
 Y.S. Kupitz: ksupporting hyperplanes of a finite set in
dspace.
 Abstract:
The main result is that for all k,d ≥ 1 any set of
[1/2(d + 1)k] + 1 affinely independent points in dspace 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.
 Y.S. Kupitz and M.A. Perles: Locally symmetric graphs.
 Abstract:
An nregular graph G is locally symmetric if
Aut(G) acts as S_{n}
on the n neighbours of each vertex.
The authors classify such graphs having 4cycles 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.
 A. Lubotzky and S. Mozes: Vanishing of matrix coefficients for
representations of tree automeorisms.
 Abstract:
An analogue of the HoweMoore 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 nonzero vectors the matrix coefficients tend to zero at
infinity.
 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.
 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.
 B. Peleg and J. Rosenmüller: The leastcore, 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 constantsum 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.
 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
Rtrees.
 Z. Sela: The homeomorphism problem for geometric 3manifolds 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 3manifolds satisfying
a weaker hypothesis than the Thurston geometrization conjecture. The paper uses
MakaninRazbarov algorithm for solving equations in free groups as well as
techniques from group actions on trees and 3dimensional topology.
 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 3manifold 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.
 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 Rmodules 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.
