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1.
Necdet Güner 《Geometriae Dedicata》1996,63(1):17-23
Let N=G/ be a compact nilmanifold, G a connected, simply connected, nilpotent Lie group with its discrete subgroup and Lie algebra
. Let I* (
) denote the invariant differential forms on
.If I* (
) H* (
) is an injective map, then G is abelian and N is a torus. Furthermore, N has a formal minimal model. If N is an even-dimensional compact nilmanifold, it has a Kähler structure and invariant symplectic structure if and only if I* (
) H* (
) is injective. 相似文献
2.
Zhen-Qing Chen 《Potential Analysis》1996,5(4):383-401
Let D be an open set in d and E be a relatively closed subset of D having zero Lebesgue measure. A necessary and sufficient integral condition is given for the Sobolev spaces W
1,2 (D) and W
1,2(D\E) to be the same. The latter is equivalent to (normally) reflecting Brownian motion (RBM) on
being indistinguishable (in distribution) from RBM on
. This integral condition is satisfied, for example, when E has zero (d–1)-dimensional Hausdorff measure. Therefore it is possible to delete from D a relatively closed subset E having positive capacity but nevertheless the RBM on
is indistinguishable from the RBM on
, or equivalently, W
1,2(D\E)=W1,2(D). An example of such kind is: D=2 and E is the Cantor set. In the proof of above mentioned results, a detailed study of RBMs on general open sets is given. In particular, a semimartingale decomposition and approximation result previously proved in [3] for RBMs on bounded open sets is extended to the case of unbounded open sets.Research supported in part by NSF Grant DMS 86-57483. 相似文献
3.
Tero Kilpeläinen 《Potential Analysis》1994,3(3):265-272
We show that the solutionu of the equation
相似文献
4.
Alexander I. Kheifits 《Potential Analysis》1994,3(4):379-389
For continuous positive solutions of the equation
withp>(n+1)/2) in a half-space
+
n+1
the criterion is proved for existence of finite or infinite normal limit values at a given boundary point. 相似文献
5.
Let H1(
) be the usual Hardy space on
. We show that the couple (H1(
), L(
) is a Calderón couple. This result immediately follows from the following stronger one: Given any fH1(
) +L(
) there exist two linear operators U and V satisfying the properties: (i) Uf=Nf (Nf being the non-tangential maximal function of f) and U is contractive from H1(
) to L1(
) and also from L(
) to L(
); (ii) V(Nf)=f, V is similtaneously bounded from L1(
) to H1(
) and from L(
) to L(
) and the norms of V on these spaces are controlled by a universal constant. We also have similar results on the couple (Lp(
), BMO (
)) for every 1
相似文献 6.
Marilyn Breen 《Geometriae Dedicata》1996,60(3):283-288
Let
be a family of simple polygons in the plane. If every three (not necessarily distinct) members of
have a simply connected union and every two members of
have a nonempty intersection, then {P:P in
}
. Applying the result to a finite family
of orthogonally convex polygons, the set {C:C in
} will be another orthogonally convex polygon, and, in certain circumstances, the dimension of this intersection can be determined.Supported in part by NSF grant DMS-9207019. 相似文献
7.
In this paper we show that the local time of the Brownian motion belongs to the Sobolev space
for any p2 and 0<<1/p. In order to prove this result we first discuss the smoothness and integrability properties of the composition of the Dirac function with a Wiener integral W(h), and we show that this composition belongs to
, for any >0 and p>1 such that +1/p>1. 相似文献
8.
For semigroups (e
tA
)
t0 of operators on a Hilbert space, we give conditions guaranteeing trace estimates of the polynomial type
0$$
" align="middle" border="0">
, where
denotes the trace class. As an application we present higher order analogues of results due to E.B. Davies, B. Simon and M. van den Berg of the type
0$$
" align="middle" border="0">
, for certain unbounded domains
, e.g. spiny urchin domains. 相似文献
9.
We show three main results concerning Hamiltonicity of graphs derived from antimatroids. These results provide Gray codes for the feasible sets and basic words of antimatroids.For antimatroid (E,
), letJ(
) denote the graph whose vertices are the sets of
, where two vertices are adjacent if the corresponding sets differ by one element. DefineJ(
;k) to be the subgraph ofJ(
)2 induced by the sets in
with exactlyk elements. Both graphsJ(
) andJ(
;k) are connected, and the former is bipartite.We show that there is a Hamiltonian cycle inJ(
)×K
2. As a consequence, the ideals of any poset % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFpepuaaa!414C!\[\mathcal{P}\] may be listed in such a way that successive ideals differ by at most two elements. We also show thatJ(
;k) has a Hamilton path if (E,
) is the poset antimatroid of a series-parallel poset.Similarly, we show thatG(
)×K
2 is Hamiltonian, whereG(
) is the basic word graph of a language antimatroid (E,
). This result was known previously for poset antimatroids.Research supported in part by NSERC.Research supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant A3379. 相似文献
10.
The largest Fischer 3-transposition group M(24) acts flag-transitively on a 3-local incidence geometry
(M(24)) which is a c-extension of the dual polar space associated with the group O
7(3). The action of the simple commutator subgroup M(24) is still flag-transitive. We show that
(M(24)) is characterized by its diagram under the flag-transitivity assumption. The result implies in particular that
(M(24)) is simply connected. The geometry
(M(24)) appears as a subgeometry in the Buekenhout-Fischer 3-local geometry
(F
1) of the Monster group. The simple connectedness of
(M(24)) has played a crucial role in the characterization of
(F
1), which has been achieved recently. When determining the possible structure of the parabolic subgroups we have used an unpublished pushing-up result by U. Meierfrankenfeld.Dedicated to Professor B. Fischer on the occasion of his sixtieth birthday 相似文献
11.
Roman Drnovšek 《Integral Equations and Operator Theory》2001,39(3):253-266
Let
be a collection of bounded operators on a Banach spaceX of dimension at least two. We say that
is finitely quasinilpotent at a vectorx
0X whenever for any finite subset
of
the joint spectral radius of
atx
0 is equal 0. If such collection
contains a non-zero compact operator, then
and its commutant
have a common non-trivial invariant, subspace. If in addition,
is a collection of positive operators on a Banach lattice, then
has a common non-trivial closed ideal. This result and a recent remarkable theorem of Turovskii imply the following extension of the famous result of de Pagter to semigroups. Let
be a multiplicative semigroup of quasinilpotent compact positive operators on a Banach lattice of dimension at least two. Then
has a common non-trivial invariant closed ideal.This work was supported by the Research Ministry of Slovenia. 相似文献
12.
We introduce the notion ofweak subnormality, which generalizes subnormality in the sense that for the extension
ofT
we only require that
hold forf
; in this case we call
a partially normal extension ofT. After establishing some basic results about weak subnormality (including those dealing with the notion of minimal partially normal extension), we proceed to characterize weak subnormality for weighted shifts and to prove that 2-hyponormal weighted shifts are weakly subnormal. Let {
n
}
n=0
be a weight sequence and letW
denote the associated unilateral weighted shift on
. IfW
is 2-hyponormal thenW
is weakly subnormal. Moreover, there exists a partially normal extension
on
such that (i)
is hyponormal; (ii)
; and (iii)
. In particular, if is strictly increasing then
can be obtained as
13.
Aparna W. Higgins 《Algebra Universalis》1985,20(2):179-193
Given a group G and a descending chainG
0,G
1,...,G
n, of normal subgroups ofG, we prove that there exists a universal algebra
, such that the chain ...Wn(
)...W1(
}) W0(
)W(
) is isomorphic to the chain ...G
n ...G
1G
0G, where W(
) is the group of weak automorphisms of
, and Wn(
) is the group of weak automorphisms of
that leaves alln-ary operations fixed.We also prove that there are an infinite number of non-isomorphic algebras that satisfy the above.These results are a generalization of those proved by J. Sichler, in the special case when G=G0, and G1=G2=...=Gn=....Presented by J. Mycielski.This paper comprises part of the author's doctoral dissertation at the University of Notre Dame in 1983. The author wishes to express her deep gratitude to Professor Abraham Goetz for suggesting this problem, for being extremely generous with his time and experience, and for giving her his constant encouragement. The author also thanks the reviewer for his helpful comments. 相似文献
14.
Pawel Kröger 《Potential Analysis》1996,5(1):103-108
We study the first eigenfunction
1 of the Dirichlet Laplacian on a convex domain in Euclidean space. Elementary properties of Bessel functions yield that
if D is a sector in Euclidean plane with area 1 and the angle tends to 0. We aim to characterize those domains D such that
is large in terms of the ratio of the first eigenvalue of D and the infimum of the first eigenvalues of all subdomains D of D with given volume.Research supported by the Deutsche Forschungsgemeinschaft 相似文献
15.
Let
and
the foliations by the null geodesics of some lorentzian metricg on the torus
. We analyse how geodesic completeness properties ofg are related to the dynamics of
and
. 相似文献
16.
We obtain the asymptotic behaviour for the L
norm of the first eigenfunction of the Dirichlet Laplace operator on a conic sector over a geodesic disc
in
as
. We are led to conjecture that for an open, bounded and convex set D with inradius and diameter d,
where
and
相似文献
17.
Dr. Detlev Poguntke 《Monatshefte für Mathematik》1976,82(1):31-50
This is a continuation of the paper Zwei Klassen lokalkompakter maximal fastperiodischer Gruppen, [6]. In [6], the classes
and
were introduced. We give sufficient conditions to conclude thatG is in
if one knows thatG/G
0 is in
. If a groupG is in
and ifG satisfies the Chu-duality then all closed subgroups ofG satisfy the Chu-duality. The Chu-quasi-dual of the Heisenberg groupH with integral coefficients is computed. It is shown thatH does not satisfy the Chu-duality, thatH is in
, and thatH is not in
. 相似文献
18.
G. L. Booth 《Periodica Mathematica Hungarica》1991,22(3):175-182
The Brown-McCoy radical
is known to be an ideal-hereditary Kurosh-Amitsur radical in the variety of zerosymmetric near-rings. We define the Brown-McCoy and simplical radicals,
and
, respectively, for zerosymmetric -near-rings. Both
and
are ideal-hereditary Kurosh-Amitsur radicals in that variety. IfM is a zerosymmetric -near-ring with left operator near-ringL, it is shown that
, with equality ifM has a strong left unity.
is extended to the variety of arbitrary near-rings, and
and
are extended to the variety of arbitrary -near-rings, in a way that they remain Kurosh-Amitsur radicals. IfN is a near-ring andA N, then
, with equality ifA if left invariant. 相似文献
19.
In this paper we investigate functorial properties of the Segal algebra
which consists of all functionsf in Wiener's algebra onG with Fourier transform
in Wiener's algebra on the dual group
. Especially
may serve as a very large and natural domain for Poisson's formula. Moreover, there is introduced a Segal algebraE
0(G) containing
as a subspace, but still eachfE
0(S) satisfies Poisson's formula. 相似文献
20.
Andreas Blass 《Archive for Mathematical Logic》1990,30(1):1-11
We prove several theorems about the cardinal
associated with groupwise density. With respect to a natural ordering of families of nond-ecreasing maps from to, all families of size
are below all unbounded families. With respect to a natural ordering of filters on, all filters generated by
sets are below all non-feeble filters. If
then
and
. (The definitions of these cardinals are recalled in the introduction.) Finally, some consequences deduced from
by Laflamme are shown to be equivalent to
. 相似文献
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